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is a system composed of a weight and a string. The string is attached at the top end to a pivot and at the bottom end to a weight. Being inextensible, the string has a constant length. Therefore, this system is scleronomous; it obeys the scleronomic constraint
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Although the top end of the string is not fixed, the length of this inextensible string is still a constant. The distance between the top end and the weight must stay the same. Therefore, this system is rheonomous; it obeys the rheonomic constraint
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Constraints are further classified according as the equations of constraint contain the time as an explicit variable (rheonomous) or are not explicitly dependent on time (scleronomous).
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Theory and
Problems of THEORETICAL MECHANICS with an Introduction to Lagrange's Equations and Hamiltonian Theory
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The situation changes if the pivot point is moving, e.g. undergoing a
492:(2nd ed.). United States of America: Addison Wesley. p.
436:{\displaystyle {\sqrt {(x-x_{0}\cos \omega t)^{2}+y^{2}}}-L=0\,\!}
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Mechanical system whose constraints are dependent on time
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129:{\displaystyle {\sqrt {x^{2}+y^{2}}}-L=0\,\!}
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58:Example: simple 2D pendulum
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459:Holonomic constraints
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48:rheonomic constraints
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454:Lagrangian mechanics
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488:Classical Mechanics
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52:scleronomous
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553:scleronomic
40:constraints
576:Categories
465:References
36:rheonomous
582:Mechanics
561:rheonomic
420:−
389:ω
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311:ω
253:ω
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484:(1980).
448:See also
72:pendulum
44:variable
547:) or (
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347:time.
274:where
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140:where
529:ISBN
498:ISBN
383:cos
247:cos
34:is
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