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715:{\displaystyle {\begin{aligned}{\boldsymbol {\psi }}_{P}&={\frac {\partial \mathbf {v} _{P}}{\partial t}}\\&={\boldsymbol {\psi }}_{C}+{\boldsymbol {\alpha }}\times (\mathbf {r} _{P}-\mathbf {r} _{C})\end{aligned}}}
78:, the study of rigid body motion allows for several ways to define the acceleration of a body. The usual definition of acceleration entails following a single particle/point of a rigid body and observing its changes in
481:{\displaystyle \mathbf {a} _{P}={\frac {d\mathbf {v} _{P}}{dt}}=\mathbf {a} _{C}+{\boldsymbol {\alpha }}\times (\mathbf {r} _{P}-\mathbf {r} _{C})+{\boldsymbol {\omega }}\times (\mathbf {v} _{P}-\mathbf {v} _{C})}
591:
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for robotic applications. The author also chooses to use spatial accelerations extensively in place of material accelerations as they simplify the equations and allows for compact notation. See
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280:{\displaystyle \mathbf {v} _{P}=\mathbf {v} _{C}+{\boldsymbol {\omega }}\times (\mathbf {r} _{P}-\mathbf {r} _{C})}
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884:{\displaystyle {\boldsymbol {\psi }}_{P}=\mathbf {a} _{P}-{\boldsymbol {\omega }}\times \mathbf {v} _{P}}
90:, where typically one measures velocity and/or acceleration at a fixed point inside a testing apparatus.
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82:. Spatial acceleration entails looking at a fixed (unmoving) point in space and observing the change in
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of the particles that pass through that point. This is similar to the definition of acceleration in
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This reference defines spatial accelerations for use in rigid body mechanics.
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on the body being a function of the position and velocity of a center-point
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JPL DARTS page has a section on spatial operator algebra (link:
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Consider a moving rigid body and the velocity of a point
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which is similar to the velocity transformation above.
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749:{\displaystyle {\boldsymbol {\psi }}_{P}}
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62:Learn how and when to remove this message
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505:{\displaystyle {\boldsymbol {\alpha }}}
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970:This reference effectively combines
760:that is moving with linear velocity
727:In general the spatial acceleration
512:is the angular acceleration vector.
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1002:Springer Handbook of Robotics
980:online presentation, page 23
939:. McGraw-Hill Professional.
131:The linear velocity vector
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956:Robot Dynamics Algorithms
954:Roy Featherstone (1987).
515:The spatial acceleration
106:and the angular velocity
1005:. Springer. p. 41.
34:may need to be rewritten
935:Frank M. White (2003).
982:also from same author.
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42:and read the
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1036:Acceleration
1031:Rigid bodies
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972:screw theory
958:. Springer.
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52:January 2017
49:
38:Please help
33:
31:lead section
1025:Categories
929:References
917:April 2012
94:Definition
867:×
863:ω
859:−
834:ψ
737:ψ
691:−
673:×
669:α
655:ψ
634:∂
617:∂
597:ψ
558:ψ
525:ψ
499:α
461:−
443:×
439:ω
417:−
399:×
395:α
298:ω
260:−
242:×
238:ω
115:ω
999:(2008).
976:dynamics
84:velocity
80:velocity
76:physics
1009:
962:
943:
490:where
289:where
1007:ISBN
960:ISBN
941:ISBN
822:as:
581:as:
322:is:
314:The
197:as:
912:.
818:at
577:at
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128:.
74:In
1027::
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1015:.
968:.
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915:(
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854:P
849:a
844:=
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742:P
706:)
701:C
696:r
686:P
681:r
676:(
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650:=
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627:P
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611:=
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563:C
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476:)
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466:v
456:P
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446:(
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376:=
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344:=
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245:(
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219:=
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195:C
179:C
174:v
162:P
146:P
141:v
104:C
100:P
65:)
59:(
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50:(
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36:.
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