166:"Many important discoveries have been made when scientists commenced their work as if their theoretically postulated models of atoms, viruses, vitamins, hormones, and genes had actual, real world substantial existence. They proceeded as though each imaginary concept actually existed in precisely the form their theoretical speculation outlined; and, discarding any pretence of analogy, they proceeded with the view that the substantial, real world was exactly as they had theoretically described it. ... Consider the analogue model advanced to assist understanding of the behaviour of gases which suggests possible relationships between some theoretical activities of gas particles and some observable activities of billiard-balls. Achinstein (1964, p.332) reminds us that, despite thinking about gases in this useful way, "the physicist obviously supposes that molecules, not billiard balls, comprise gases" — Yeates (2004, pp.71, 73)
1279:, there is the question of how the physical/biological laws of the target system relate to the analogical models created by humans to represent the target system. We seem to assume that the process of constructing analogical models gives us access to the fundamental laws governing the target system. However strictly speaking we only have empirical knowledge of the laws that hold true for the analogical system, and if the time constant for the target system is larger than the life cycle of human being (as in the case of the geobiosphere) it is therefore very difficult for any single human to empirically verify the validity of the extension of the laws of their model to the target system in their lifetime.
153:
34:
1399:…). Similarity is implicated in this process because a successful, useful analogy depends upon there being some sort of similarity between the source domain and the target domain and because the perception of similarity is likely to play a major role in some of the key processes associated with analogical reasoning" (Vosniadou and Ortony, 1989, pp.6-7).
1158:, introduced by Henry M. Paynter in 1960. It is usual to use the force-voltage analogy (impedance analogy) with bond graphs, but it is not a requirement to do so. Likewise Trent used a different representation (linear graphs) and his representation has become associated with the force-current analogy (mobility analogy), but again this is not mandatory.
109:
Analogical models, also called "analog" or "analogue" models, seek the analogous systems that share properties with the target system as a means of representing the world. It is often practicable to construct source systems that are smaller and/or faster than the target system so that one can deduce
1062:
Maxwell's analogy was initially used merely to help explain electrical phenomena in more familiar mechanical terms. The work of
Firestone, Trent and others moved the field well beyond this, looking to represent systems of multiple energy domains as a single system. In particular, designers started
1262:
Examples are Vogel and Ewel who published 'An
Electrical Analog of a Trophic Pyramid' (1972, Chpt 11, pp. 105–121), Elmore and Sands (1949) who published circuits devised for research in nuclear physics and the study of fast electrical transients done under the Manhattan Project (however no
1153:
Many applications of dynamical models convert all energy domains in the system into an electrical circuit and then proceed to analyse the complete system in the electrical domain. There are, however, more generalised methods of representation. One such representation is through the use of
422:. In this analogy electrical impedance is made analogous to mechanical mobility (the inverse of mechanical impedance). Firestone's idea was to make analogous variables that are measured across an element, and make analogous variables that flow through an element. For instance, the
1426:"An analogue model describes specific relationships between selected components of the "original" by creating analogies with the relationships that are displayed by components in some other "secondary domain" of a totally different medium." (Yeates, 2004, p.72).
1250:
Electronic circuits were used to model and simulate engineering systems such as aeroplanes and nuclear power plants before digital computers became widely available with fast enough turn over times to be practically useful. Electronic circuit instruments called
345:
Dynamical analogies establish analogies between systems in different energy domains by means of comparison of the system dynamic equations. There are many ways such analogies can be built, but one of the most useful methods is to form analogies between pairs of
176:
used the flow of water to model economic systems (the target system); electronic circuits can be used to represent both physiological and ecological systems. When a model is run on either an analog or digital computer this is known as the process of
1161:
Some authors discourage the use of domain specific terminology for the sake of generalisation. For instance, because much of the theory of dynamical analogies arose from electrical theory the power conjugate variables are sometimes called
430:
variable current is the analogy of force. Firestone's analogy has the advantage of preserving the topology of element connections when converting between domains. A modified form of the through and across analogy was proposed in 1955 by
139:
these smaller/bigger, slower/faster systems are scaled up or down so that they match the functioning of the target system, and are therefore called analogs of the target system. Once the calibration has taken place, modellers speak of a
417:
Specifying power conjugate variables still does not result in a unique analogy, there are multiple ways the conjugates and analogies can be specified. A new analogy was proposed by Floyd A. Firestone in 1933 now known as the
397:
is the ratio of force and velocity. The concept of impedance can be extended to other domains, for instance in acoustics and fluid flow it is the ratio of pressure to rate of flow. In general, impedance is the ratio of an
214:
but does not preserve the network topology. The mobility analogy preserves the network topology but does not preserve the analogy between impedances. Both preserve the correct energy and power relationships by making
1136:
A widely used analogy in the thermal domain maps temperature difference as the effort variable and thermal power as the flow variable. Again, these are not power conjugate variables, and the ratio, known as
1086:
in electrical engineering and apply it to mechanical systems. The quality of filters required for radio applications could not be achieved with electrical components. Much better quality resonators (higher
1141:, is not really an analogy of either impedance or electrical resistance as far as energy flows are concerned. A compatible analogy could take temperature difference as the effort variable and
1234:
of an electric circuit attempts to explain circuitry intuitively in terms of plumbing, where water is analogous to the mobile sea of charge within metals, pressure difference is analogous to
1754:
814:
119:
of target system behaviour. Analog devices are therefore those in which may differ in substance or structure but share properties of dynamic behaviour (Truit and Rogers, p. 1-3).
354:. Doing so preserves the correct energy flow between domains, a useful feature when modelling a system as an integrated whole. Examples of systems that require unified modelling are
979:
864:
929:
1049:
1019:
2045:
2031:
1125:, does not measure the rate of dissipation of energy so is not a true impedance. Where a compatible analogy is required, mmf can be used as the effort variable and
60:
are a method of representing a phenomenon of the world, often called the "target system" by another, more understandable or analysable system. They are also called
1712:
Colyvan, Mark and
Ginzburg, Lev R. (2010) "Analogical Thinking in Ecology: Looking Beyond Disciplinary Boundaries", The Quarterly Review of Biology, 85(2): 171–82.
1091:) could be made with mechanical parts but there was no equivalent filter theory in mechanical engineering. It was also necessary to have the mechanical parts, the
1965:
1214:) are entities (models, representations, etc.) that can be replaced, to fulfill the same function. When the entities in question are formally represented by
1063:
converting the mechanical parts of an electromechanical system to the electrical domain so that the whole system could be analyzed as an electrical circuit.
1170:
according to whether they are analogs of voltage or current respectively in the electrical domain. Likewise, the
Hamiltonian variables are sometimes called
1121:(φ) to electric current. However, mmf and φ are not power conjugate variables. The product of these is not in units of power and the ratio, known as
984:
There is a corresponding relationship for other analogies and sets of variables. The
Hamiltonian variables are also called the energy variables. The
1951:
1391:"There is general agreement that analogical reasoning involves the transfer of relational information from a domain that already exists in memory (…
123:
dynamical analogies establish the analogies between electrical, mechanical, acoustical, magnetic and electronic systems: Olson (1958), p. 2.
195:
Any number of systems could be used for mapping electrical phenomena to mechanical phenomena, but two principle systems are commonly used: the
2017:
1762:
1745:
1192:
750:
are equal to the power conjugate variables. The
Hamiltonian variables are so called because they are the variables which usually appear in
347:
216:
190:
2063:
1095:, and the electrical components of the circuit analyzed as a complete system in order to predict the overall response of the filter.
2000:
1959:
1895:
1705:
1789:
1304:
2043:
1866:
1823:
1808:
1690:
1675:
1660:
1645:
135:
might then represent the arithmetic operations (addition, subtraction, multiplication, and division). Through the process of
1267:(1994) who published circuits devised to analogically model ecological-economic systems at many scales of the geobiosphere.
152:
817:
144:
between the primary system and its analog. Thus the behaviour of two systems can be determined by experimenting with one.
2071:
68:
172:
A mechanical device can be used to represent mathematical calculations. For instance, the
Phillips Hydraulic Computer
2010:
1942:
1714:
293:
can be described by analogous equations on a geometrical basis, almost without regard to the physical details about
2095:
1749:, National Nuclear Energy Series, Manhattan Project Technical Section, Division V, Vol. 1, New York: McGraw-Hill.
112:
106:
system), in order "to illustrate some particular aspect (or clarify selected attributes) of the primary domain".
2006:
1934:
1683:
Technology for
Modelling: Electrical Analogies, Engineering Practice, and the Development of Analogue Computing
776:
443:
Comparison of various power conjugate analogies for electrical, mechanical, rotational, and fluid flow domains
27:
1200:
1768:
1222:
is related to "same behavior": they take the same output sequence when submitted to the same input sequence.
1130:
988:
of a power conjugate variable with respect to a
Hamiltonian variable is a measure of energy. For instance,
2021:
932:
938:
823:
891:
870:
751:
309:
132:
33:
1737:
1376:
624:
394:
390:
211:
207:
2026:
1294:
1122:
1114:
378:
366:
276:
20:
1071:, and a coherent presentation of this method was presented in a 1925 paper by Clifford A. Nickle.
203:. The impedance analogy maps force to voltage whereas the mobility analogy maps force to current.
2100:
1983:
1721:
1138:
746:
The
Hamiltonian variables, also called the energy variables, are those variables which when time-
305:
46:
38:
1024:
994:
1377:"Mechanisms of Analogical Learning", pp.199-241, in Stella Vosniadou and Andrew Ortony (eds.),
1955:
1938:
1891:
1862:
1847:
1819:
1804:
1758:
1701:
1686:
1671:
1656:
1641:
1231:
1101:
helped popularise the use of dynamical analogies in the audio electronics field with his book
1075:
1068:
407:
359:
333:
229:
196:
2090:
1920:, Graduate Diploma in Arts (By Research) Dissertation, University of New South Wales, 2004.
1877:
1785:
1776:
1728:
1627:
1619:
1299:
1256:
1239:
1178:
according to whether they are analogs of momentum or displacement in the mechanical domain.
615:
600:
419:
411:
382:
298:
290:
233:
200:
1950:. G - Reference, Information and Interdisciplinary Subjects Series (illustrated ed.).
1944:
Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics
377:. This analogy became so widespread that sources of voltage are still today referred to as
2075:
2049:
1995:
1718:
1263:
circuits having application to weapon technology were included for security reasons), and
1252:
755:
432:
351:
280:
406:
variable that results. For this reason, the Maxwell analogy is often referred to as the
1916:
Yeates, Lindsay B. (2004), "Comparative Cognitive Processes", pp.40-76 in L.B. Yeates,
1839:
1829:
1264:
1129:(rate of change of magnetic flux) will then be the flow variable. This is known as the
1098:
2084:
1741:
1372:
1118:
1083:
1079:
1064:
254:
250:
1275:
The process of analogical modelling has philosophical difficulties. As noted in the
1199:
containing resistances only, with voltage and current sources, can be replaced to a
1939:"Chapter 12: Parallel Addition, Series-Parallel Duality, and Financial Mathematics"
1769:"Lumped equivalent circuits of magnetic components: the gyrator-capacitor approach"
1309:
1255:
were used to speed up circuit construction time. However analog computers like the
1191:
763:
355:
160:
Many different instruments and systems can be used to create an analogical model.
1344:
1319:
286:
136:
79:
42:
869:
In the translational mechanical domain, the Hamiltonian variables are distance
2068:
1155:
1092:
747:
325:
178:
1082:, widely used these analogies in order to take the well -developed theory of
1881:
1215:
985:
321:
313:
258:
116:
76:
1872:
Smith, Malcolm C. (2002) "Synthesis of mechanical networks: the inerter]",
94:
is the process of representing information about a particular subject (the
1711:
1339:
1334:
1324:
1088:
878:
591:
386:
272:
237:
1851:
90:
A simple type of analogy is one that is based on shared properties; and
1915:
1314:
1289:
1235:
1142:
374:
128:
91:
1780:
1725:
1329:
582:
329:
173:
410:, although the concept of impedance was not conceived until 1886 by
1834:
Ecological and General Systems: and introduction to systems ecology
1732:
1631:
1190:
370:
294:
2064:
Stanford Encyclopedia of Philosophy entry on Models in Science
1067:
was a pioneer of this kind of modelling in his development of
49:
with an equivalent structure and behaviour (bottom), then, an
1910:
A Model Menagerie: Laboratory Studies about Living Systems
754:. The Hamiltonian variables in the electrical domain are
636:
Table of equivalents under the through and across system
1755:
Ecological Orbits: How Planets Move and Populations Grow
1259:
could also consist of gears and pulleys in calculation.
127:
For example, in analog electronic circuits, one can use
16:
Relation of types of systems with corresponding dynamics
324:
requires a similarity within a situation; for example,
1876:, vol. 47, iss. 10, pp. 1648–1662, October 2002.
1027:
997:
941:
894:
826:
779:
426:
variable voltage is the analogy of velocity, and the
1435:
Ginzburg and Colyvan 2004; Colyvan and Ginzburg 2010
393:
is the ratio of voltage and current, so by analogy,
206:
The impedance analogy preserves the analogy between
1043:
1013:
973:
923:
858:
808:
385:which, in the Maxwell analogy, maps to mechanical
350:. That is, a pair of variables whose product is
121:
75:representations (see illustration) if they are
1670:, Springer Science & Business Media, 1999
1918:Thought Experimentation: A Cognitive Approach
8:
1814:Martinsen, Orjan G.; Grimnes, Sverre (2011)
1626:, Vol.31, No.4, (October 1964), pp.328-350.
236:might perform the mathematical operation of
1905:, John F. Rider Publishing, Inc., New York.
1790:A gravitational and electromagnetic analogy
1622:(1964), "Models, Analogies, and Theories",
1113:A common analogy of magnetic circuits maps
102:system) by another particular subject (the
312:arise that are the same as those found in
2025:
2011:"Introduction to Series-Parallel Duality"
1952:Rowman & Littlefield Publishers, Inc.
1034:
1026:
1004:
996:
942:
940:
895:
893:
827:
825:
809:{\displaystyle {\frac {d\lambda }{dt}}=v}
780:
778:
1381:, Cambridge: Cambridge University Press.
1238:, and water's flow rate is analogous to
1074:From the 1950s onward, manufacturers of
634:
441:
316:, albeit with different interpretations.
285:For example, the inverse-square laws of
151:
32:
1886:Taylor, John T.; Huang, Qiuting (1997)
1753:Ginzburg, Lev and Colyvan, Mark (2004)
1668:Electromechanical Sensors and Actuators
1356:
336:by using the concept of myriad myriads.
2069:Interdisciplinary Electrical Analogies
1991:
1981:
1874:IEEE Transactions on Automatic Control
1816:Bioimpedance and Bioelectricity Basics
1801:Signal And Image Processing Sourcebook
1773:IEEE Transactions on Power Electronics
142:one-to-one correspondence in behaviour
2018:University of California at Riverside
131:to represent an arithmetic quantity;
7:
1757:, Oxford University Press, New York.
1747:Electronics: Experimental Techniques
1363:Stanford Encyclopedia of Philosophy.
381:. The power conjugate of voltage is
369:who, in 1873, associated mechanical
365:The earliest such analogy is due to
156:The Mechanism of the Analogue Model.
1775:, vol. 8, iss. 2, pp. 97–103.
1395:…) to the domain to be explained (…
1379:Similarity and Analogical Reasoning
1277:Stanford Encyclopedia of Philosophy
974:{\displaystyle {\frac {dx}{dt}}=u.}
859:{\displaystyle {\frac {dq}{dt}}=i.}
456:Through and across analogy (Trent)
435:and is the modern understanding of
414:, some time after Maxwell's death.
334:number of grains of sand on a beach
1888:CRC Handbook of Electrical Filters
924:{\displaystyle {\frac {dp}{dt}}=F}
461:Effort or across power conjugates
14:
509:Flow or through power conjugates
1145:flow rate as the flow variable.
1054:are both expressions of energy.
2034:from the original on 2019-08-10
1971:from the original on 2016-03-05
1638:Mechatronics: An Introduction,
1465:Martinsen & Grimnes, p. 287
1305:General purpose analog computer
191:Mechanical–electrical analogies
1846:, 2nd ed., Van Nostrand, 1958
1:
1109:Non-power-conjugate analogies
933:Newton's second law of motion
1836:, Colorado University Press.
1203:, to show the same behavior.
1182:Electronic circuit analogies
453:Mobility analogy (Firestone)
257:as a proxy for the study of
148:Creating an analogical model
1857:Regtien, Paul P. L. (2002)
1201:Thévenin equivalent circuit
450:Impedance analogy (Maxwell)
2117:
1903:Basics of analog computers
1698:RF Components and Circuits
1666:Busch-Vishniac, Ilene J.,
1651:Borutzky, Wolfgang (2009)
1546:Taylor & Huang, p. 378
1044:{\displaystyle \int u\,dp}
1014:{\displaystyle \int F\,dx}
818:Faraday's law of induction
188:
25:
18:
2007:Ellerman, David Patterson
1935:Ellerman, David Patterson
1636:Bishop, Robert H. (2005)
1498:Busch-Vishniac, pp. 18-20
1105:first published in 1943.
348:power conjugate variables
1901:Truit and Rogers (1960)
1890:, Boca Raton: CRC Press
1859:Sensors for Mechatronics
1767:Hamill, David C. (1993)
1653:Bond Graph Methodology,
1176:generalised displacement
219:of variables analogous.
28:Analogy (disambiguation)
19:Not to be confused with
1882:10.1109/TAC.2002.803532
1854:(first published 1943).
1696:Carr, Joseph J. (2002)
1271:Philosophical conundrum
1131:gyrator-capacitor model
245:Physiological analogies
1908:Vogel and Ewel (1972)
1799:Libbey, Robert (1994)
1204:
1045:
1015:
975:
925:
860:
810:
700:Mechanical rotational
310:differential equations
253:used the study of the
157:
133:operational amplifiers
125:
54:
1681:Care, Charles (2010)
1624:Philosophy of Science
1582:Busch-Vishniac, p. 19
1516:Busch-Vishniac, p. 21
1486:Busch-Vishniac, p. 19
1459:Busch-Vishniac, p. 20
1444:Busch-Vishniac, p. 18
1194:
1117:(mmf) to voltage and
1046:
1016:
976:
926:
861:
811:
752:Hamiltonian mechanics
742:Hamiltonian variables
712:Moment of inertia (I)
217:power conjugate pairs
155:
36:
1417:Yeates (2004), p.73.
1408:Yeates (2004), p.71.
1212:functional analogues
1172:generalised momentum
1025:
995:
939:
892:
824:
777:
706:Angular velocity (ω)
631:Table of equivalents
625:volumetric flow rate
395:mechanical impedance
391:Electrical impedance
212:mechanical impedance
208:electrical impedance
185:Mechanical analogies
41:diagram of a simple
26:For other uses, see
1844:Dynamical Analogies
1606:Borutzky, pp. 27-28
1525:Borutzky, pp. 27-28
1295:Conceptual metaphor
1123:magnetic reluctance
1115:magnetomotive force
1103:dynamical analogies
655:Energy dissipation
637:
444:
379:electromotive force
367:James Clerk Maxwell
341:Dynamical analogies
62:dynamical analogies
21:Analogical modeling
2074:2010-05-13 at the
2048:2019-08-10 at the
1954:pp. 237–268.
1738:Elmore, William C.
1717:2023-04-07 at the
1246:Analogue computers
1208:Functional analogs
1205:
1187:Functional analogs
1139:thermal resistance
1076:mechanical filters
1069:analogue computers
1041:
1011:
971:
921:
856:
806:
709:Torsion spring (Îş)
680:Mechanical linear
635:
442:
437:through and across
306:population ecology
158:
80:isomorphic systems
55:
47:electrical network
39:mechanical network
2096:Scientific models
1912:, Addison-Wesley.
1861:, Elsevier, 2012
1818:, Academic Press
1786:Heaviside, Oliver
1781:10.1109/63.223957
1763:978-0-1980-3754-5
1700:, Oxford: Newnes
1620:Achinstein, Peter
1549:Carr, pp. 170–171
1232:hydraulic analogy
1226:Hydraulic analogy
1218:, the concept of
960:
913:
845:
798:
739:
738:
560:
559:
408:impedance analogy
402:variable and the
360:audio electronics
230:hydraulic analogy
223:Hydraulic analogy
197:impedance analogy
58:Analogical models
2108:
2042:
2040:
2039:
2029:
2015:
1999:
1993:
1989:
1987:
1979:
1977:
1976:
1970:
1949:
1607:
1604:
1598:
1595:
1589:
1577:
1571:
1568:
1562:
1559:
1553:
1541:
1535:
1532:
1526:
1523:
1517:
1514:
1508:
1507:Olson, pp. 27-29
1505:
1499:
1496:
1490:
1475:
1469:
1451:
1445:
1442:
1436:
1433:
1427:
1424:
1418:
1415:
1409:
1406:
1400:
1389:
1383:
1370:
1364:
1361:
1300:Conceptual model
1257:Norden bombsight
1253:analog computers
1240:electric current
1050:
1048:
1047:
1042:
1020:
1018:
1017:
1012:
980:
978:
977:
972:
961:
959:
951:
943:
930:
928:
927:
922:
914:
912:
904:
896:
884:
876:
865:
863:
862:
857:
846:
844:
836:
828:
815:
813:
812:
807:
799:
797:
789:
781:
769:
761:
652:Energy storage 2
649:Energy storage 1
643:Through variable
638:
616:angular velocity
601:electric current
445:
420:mobility analogy
412:Oliver Heaviside
383:electric current
373:with electrical
291:electromagnetism
266:Formal analogies
234:water integrator
201:mobility analogy
2116:
2115:
2111:
2110:
2109:
2107:
2106:
2105:
2081:
2080:
2076:Wayback Machine
2060:
2055:
2050:Wayback Machine
2037:
2035:
2013:
2005:
1990:
1980:
1974:
1972:
1968:
1962:
1947:
1933:
1929:
1927:Further reading
1924:
1840:Olson, Harry F.
1830:Odum, Howard T.
1794:The Electrician
1719:Wayback Machine
1615:
1610:
1605:
1601:
1596:
1592:
1588:
1578:
1574:
1569:
1565:
1560:
1556:
1552:
1542:
1538:
1533:
1529:
1524:
1520:
1515:
1511:
1506:
1502:
1497:
1493:
1489:
1476:
1472:
1468:
1452:
1448:
1443:
1439:
1434:
1430:
1425:
1421:
1416:
1412:
1407:
1403:
1390:
1386:
1371:
1367:
1362:
1358:
1354:
1349:
1285:
1273:
1248:
1228:
1189:
1184:
1151:
1111:
1060:
1023:
1022:
993:
992:
952:
944:
937:
936:
905:
897:
890:
889:
882:
874:
837:
829:
822:
821:
790:
782:
775:
774:
767:
759:
744:
646:Across variable
633:
433:Horace M. Trent
343:
281:Richard Feynman
268:
247:
225:
193:
187:
150:
88:
31:
24:
17:
12:
11:
5:
2114:
2112:
2104:
2103:
2098:
2093:
2083:
2082:
2079:
2078:
2066:
2059:
2058:External links
2056:
2054:
2053:
2027:10.1.1.90.3666
2003:
1960:
1937:(1995-03-21).
1930:
1928:
1925:
1923:
1922:
1913:
1906:
1899:
1884:
1870:
1855:
1837:
1827:
1812:
1797:
1783:
1765:
1751:
1742:Sands, Matthew
1735:
1733:10.1086/652321
1709:
1694:
1679:
1664:
1649:
1634:
1632:10.1086/288018
1616:
1614:
1611:
1609:
1608:
1599:
1597:Bishop, p. 8.8
1590:
1587:
1586:
1585:Regtien, p. 21
1583:
1579:
1572:
1563:
1554:
1551:
1550:
1547:
1543:
1536:
1527:
1518:
1509:
1500:
1491:
1488:
1487:
1484:
1483:Smith, p. 1648
1481:
1480:Bishop, p. 8.2
1477:
1470:
1467:
1466:
1463:
1462:Smith, p. 1648
1460:
1457:
1456:Bishop, p. 8.4
1453:
1446:
1437:
1428:
1419:
1410:
1401:
1384:
1373:Gentner, Dedre
1365:
1355:
1353:
1350:
1348:
1347:
1342:
1337:
1332:
1327:
1322:
1317:
1312:
1307:
1302:
1297:
1292:
1286:
1284:
1281:
1272:
1269:
1265:Howard T. Odum
1247:
1244:
1227:
1224:
1188:
1185:
1183:
1180:
1150:
1149:Generalisation
1147:
1110:
1107:
1099:Harry F. Olson
1059:
1058:Practical uses
1056:
1052:
1051:
1040:
1037:
1033:
1030:
1010:
1007:
1003:
1000:
982:
981:
970:
967:
964:
958:
955:
950:
947:
920:
917:
911:
908:
903:
900:
867:
866:
855:
852:
849:
843:
840:
835:
832:
805:
802:
796:
793:
788:
785:
748:differentiated
743:
740:
737:
736:
733:
730:
727:
724:
721:
717:
716:
715:Rotary damper
713:
710:
707:
704:
701:
697:
696:
693:
690:
687:
684:
681:
677:
676:
673:
670:
667:
664:
661:
657:
656:
653:
650:
647:
644:
641:
632:
629:
628:
627:
618:
609:
603:
594:
585:
576:
570:
564:
558:
557:
540:
523:
510:
506:
505:
492:
479:
462:
458:
457:
454:
451:
448:
342:
339:
338:
337:
319:
318:
317:
302:
275:have the same
267:
264:
263:
262:
246:
243:
242:
241:
224:
221:
189:Main article:
186:
183:
170:
169:
168:
167:
149:
146:
87:
84:
45:(top) and one
15:
13:
10:
9:
6:
4:
3:
2:
2113:
2102:
2099:
2097:
2094:
2092:
2089:
2088:
2086:
2077:
2073:
2070:
2067:
2065:
2062:
2061:
2057:
2051:
2047:
2044:
2033:
2028:
2023:
2019:
2012:
2009:(May 2004) .
2008:
2004:
2001:
1997:
1985:
1967:
1963:
1961:0-8476-7932-2
1957:
1953:
1946:
1945:
1940:
1936:
1932:
1931:
1926:
1921:
1919:
1914:
1911:
1907:
1904:
1900:
1897:
1896:0-8493-8951-8
1893:
1889:
1885:
1883:
1879:
1875:
1871:
1868:
1864:
1860:
1856:
1853:
1849:
1845:
1841:
1838:
1835:
1831:
1828:
1825:
1821:
1817:
1813:
1810:
1806:
1802:
1798:
1795:
1791:
1787:
1784:
1782:
1778:
1774:
1770:
1766:
1764:
1760:
1756:
1752:
1750:
1748:
1743:
1739:
1736:
1734:
1730:
1727:
1723:
1720:
1716:
1713:
1710:
1707:
1706:0-7506-4844-9
1703:
1699:
1695:
1692:
1688:
1684:
1680:
1677:
1673:
1669:
1665:
1662:
1658:
1654:
1650:
1647:
1643:
1639:
1635:
1633:
1629:
1625:
1621:
1618:
1617:
1612:
1603:
1600:
1594:
1591:
1584:
1581:
1580:
1576:
1573:
1570:Hamill, p. 97
1567:
1564:
1561:Libbey, p. 13
1558:
1555:
1548:
1545:
1544:
1540:
1537:
1531:
1528:
1522:
1519:
1513:
1510:
1504:
1501:
1495:
1492:
1485:
1482:
1479:
1478:
1474:
1471:
1464:
1461:
1458:
1455:
1454:
1450:
1447:
1441:
1438:
1432:
1429:
1423:
1420:
1414:
1411:
1405:
1402:
1398:
1394:
1388:
1385:
1382:
1380:
1374:
1369:
1366:
1360:
1357:
1351:
1346:
1343:
1341:
1338:
1336:
1333:
1331:
1328:
1326:
1323:
1321:
1318:
1316:
1313:
1311:
1308:
1306:
1303:
1301:
1298:
1296:
1293:
1291:
1288:
1287:
1282:
1280:
1278:
1270:
1268:
1266:
1260:
1258:
1254:
1245:
1243:
1241:
1237:
1233:
1225:
1223:
1221:
1217:
1213:
1209:
1202:
1198:
1193:
1186:
1181:
1179:
1177:
1173:
1169:
1165:
1159:
1157:
1148:
1146:
1144:
1140:
1134:
1132:
1128:
1124:
1120:
1119:magnetic flux
1116:
1108:
1106:
1104:
1100:
1096:
1094:
1090:
1085:
1084:filter design
1081:
1080:Collins Radio
1077:
1072:
1070:
1066:
1065:Vannevar Bush
1057:
1055:
1038:
1035:
1031:
1028:
1008:
1005:
1001:
998:
991:
990:
989:
987:
968:
965:
962:
956:
953:
948:
945:
934:
918:
915:
909:
906:
901:
898:
888:
887:
886:
880:
872:
853:
850:
847:
841:
838:
833:
830:
819:
803:
800:
794:
791:
786:
783:
773:
772:
771:
765:
757:
753:
749:
741:
734:
731:
728:
725:
722:
719:
718:
714:
711:
708:
705:
702:
699:
698:
694:
691:
688:
685:
682:
679:
678:
675:Resistor (R)
674:
671:
669:Capacitor (C)
668:
665:
662:
659:
658:
654:
651:
648:
645:
642:
640:
639:
630:
626:
622:
619:
617:
613:
610:
607:
604:
602:
598:
595:
593:
589:
586:
584:
580:
577:
574:
571:
568:
565:
562:
561:
556:
552:
548:
544:
541:
539:
535:
531:
527:
524:
522:
518:
514:
511:
508:
507:
504:
500:
496:
493:
491:
487:
483:
480:
478:
474:
470:
466:
463:
460:
459:
455:
452:
449:
447:
446:
440:
438:
434:
429:
425:
421:
415:
413:
409:
405:
401:
396:
392:
388:
384:
380:
376:
372:
368:
363:
361:
357:
353:
349:
340:
335:
332:to count the
331:
327:
323:
320:
315:
311:
307:
303:
300:
296:
292:
288:
284:
283:
282:
278:
274:
270:
269:
265:
260:
256:
255:visual system
252:
251:Francis Crick
249:
248:
244:
239:
235:
231:
227:
226:
222:
220:
218:
213:
209:
204:
202:
198:
192:
184:
182:
180:
175:
165:
164:
163:
162:
161:
154:
147:
145:
143:
138:
134:
130:
124:
120:
118:
115:
114:
107:
105:
101:
97:
93:
85:
83:
81:
78:
74:
70:
65:
63:
59:
52:
48:
44:
40:
35:
29:
22:
2036:. Retrieved
1973:. Retrieved
1943:
1917:
1909:
1902:
1887:
1873:
1858:
1843:
1833:
1815:
1800:
1793:
1772:
1746:
1697:
1682:
1667:
1652:
1637:
1623:
1613:Bibliography
1602:
1593:
1575:
1566:
1557:
1539:
1530:
1521:
1512:
1503:
1494:
1473:
1449:
1440:
1431:
1422:
1413:
1404:
1396:
1392:
1387:
1378:
1368:
1359:
1310:Homomorphism
1276:
1274:
1261:
1249:
1229:
1219:
1211:
1207:
1206:
1196:
1175:
1171:
1167:
1163:
1160:
1152:
1135:
1126:
1112:
1102:
1097:
1073:
1061:
1053:
983:
871:displacement
868:
764:flux linkage
745:
726:Pressure (p)
686:Velocity (u)
672:Inductor (L)
620:
611:
605:
596:
587:
578:
572:
566:
554:
550:
546:
542:
537:
533:
529:
525:
520:
516:
512:
502:
498:
494:
489:
485:
481:
476:
472:
468:
464:
436:
427:
423:
416:
403:
399:
364:
356:mechatronics
344:
205:
194:
171:
159:
141:
126:
122:
111:
108:
103:
99:
95:
89:
72:
69:open systems
66:
61:
57:
56:
50:
2002:(271 pages)
1992:|work=
1803:, Springer
1685:, Springer
1534:Care, p. 76
1345:Wind tunnel
1320:Isomorphism
1230:A fluid or
1216:black boxes
1156:bond graphs
1093:transducers
723:Volume flow
695:Damper (B)
666:Voltage (V)
663:Current (I)
660:Electrical
608:is velocity
287:gravitation
238:integration
137:calibration
92:analogizing
86:Explanation
2085:Categories
2052:(24 pages)
2038:2019-08-09
1975:2019-08-09
1867:0123944090
1824:0080568807
1809:0442308612
1691:1848829485
1676:038798495X
1661:1848828829
1646:1420037242
1640:CRC Press
1352:References
1078:, notably
885:) because
770:) because
720:Hydraulic
703:Torque (T)
689:Spring (K)
569:is voltage
326:Archimedes
271:"The same
179:simulation
2101:Semantics
2022:CiteSeerX
1994:ignored (
1984:cite book
1655:Springer
1197:black box
1029:∫
999:∫
986:integrand
787:λ
683:Force (F)
328:used the
322:Recursion
314:mechanics
277:solutions
273:equations
259:awareness
117:knowledge
77:black box
43:resonator
2072:Archived
2046:Archived
2032:Archived
1966:Archived
1788:(1893) "
1715:Archived
1375:(1989),
1340:Paradigm
1335:Morphism
1325:Metaphor
1283:See also
1089:Q factor
879:momentum
692:Mass (M)
592:pressure
575:is force
387:velocity
199:and the
113:a priori
96:analogue
2091:Analogy
1852:1450867
1842:(1958)
1832:(1994)
1744:(1949)
1315:Inquiry
1290:Analogy
1236:voltage
1143:entropy
935:), and
820:), and
428:through
375:voltage
299:charges
129:voltage
53:for it.
2024:
1958:
1894:
1865:
1850:
1822:
1807:
1761:
1726:652321
1724:
1704:
1689:
1674:
1659:
1644:
1397:target
1393:source
1330:MONIAC
1220:analog
1168:I-type
1164:V-type
877:) and
762:) and
756:charge
735:Valve
583:torque
424:across
400:effort
330:myriad
295:masses
279:." --
174:MONIAC
104:target
100:source
73:analog
51:analog
2014:(PDF)
1969:(PDF)
1948:(PDF)
1722:JSTOR
1127:dφ/dt
563:where
519:, ω,
501:, ω,
488:, ω,
371:force
352:power
228:In a
71:have
1996:help
1956:ISBN
1892:ISBN
1863:ISBN
1848:OCLC
1820:ISBN
1805:ISBN
1759:ISBN
1740:and
1702:ISBN
1687:ISBN
1672:ISBN
1657:ISBN
1642:ISBN
1210:(or
1195:Any
1174:and
1166:and
1021:and
732:Mass
729:Tank
404:flow
358:and
297:and
289:and
232:, a
210:and
67:Two
1878:doi
1792:".
1777:doi
1729:doi
1628:doi
623:is
614:is
599:is
590:is
581:is
304:In
98:or
2087::
2030:.
2020:.
2016:.
1988::
1986:}}
1982:{{
1964:.
1941:.
1771:,
1242:.
1133:.
553:,
549:,
545:,
536:,
532:,
528:,
515:,
497:,
484:,
475:,
471:,
467:,
439:.
389:.
362:.
308:,
181:.
82:.
64:.
37:A
2041:.
1998:)
1978:.
1898:.
1880::
1869:.
1826:.
1811:.
1796:.
1779::
1731::
1708:.
1693:.
1678:.
1663:.
1648:.
1630::
1039:p
1036:d
1032:u
1009:x
1006:d
1002:F
969:.
966:u
963:=
957:t
954:d
949:x
946:d
931:(
919:F
916:=
910:t
907:d
902:p
899:d
883:p
881:(
875:x
873:(
854:.
851:i
848:=
842:t
839:d
834:q
831:d
816:(
804:v
801:=
795:t
792:d
784:d
768:λ
766:(
760:q
758:(
621:Q
612:ω
606:u
597:I
588:p
579:T
573:F
567:V
555:Q
551:T
547:F
543:I
538:p
534:T
530:F
526:I
521:Q
517:u
513:I
503:p
499:u
495:V
490:Q
486:u
482:V
477:p
473:T
469:F
465:V
301:.
261:.
240:.
30:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
