Abstract
Let G(t) be the configuration at time t of a material system \(\{\mathcal{M};d\mu \}\)in motion from its initial configuration G o . Every point P o ∈ G o follows its trajectory to arrive at the position P(t) ∈ G(t) at time t; vice versa, a point P ∈ G(t) may be regarded as originating from the motion of some P o ∈ G o .
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Notes
- 1.
If it is a continuum, then dμ(P) = ρ(P)dV (P), where ρ( ⋅) is the density and dV (P) is the Lebesgue measure of an elemental volume about P. If it is nondeformable, the configuration G(t) is obtained from G o by a rigid motion, so that the Jacobian of the transformation is one.
- 2.
A more general notion of workless that would include unilateral constraints would be that δΛ ≥ 0 for every elemental virtual displacement δP compatible with the constraints.
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DiBenedetto, E. (2011). Systems Dynamics. In: Classical Mechanics. Cornerstones. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4648-6_5
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DOI: https://doi.org/10.1007/978-0-8176-4648-6_5
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Publisher Name: Birkhäuser, Boston, MA
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