Riv. Mat. Univ. Parma, Vol. 9, No. 2, 2018
Stefano Pasquero ^{[a]}
Framing the bases of Impulsive Mechanics of constrained systems into a jetbundle geometric context
Pages: 227254
Received: 11 July 2018
Accepted in revised form: 16 November 2018
Mathematics Subject Classification (2010): 70F35, 7002, 70G45.
Keywords: Fibred spacetime, impulsive constraint, constitutive characterization.
Author address:
[a]: University of Parma, Department of Mathematical Physical and Computer Sciences, Parco Area delle Scienze 53/a (Campus), 43124 Parma, Italy
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Abstract:
We illustrate how the
different kinds of constraints acting on an impulsive mechanical
system can be described in the geometric setup given by the
configuration spacetime bundle \(\pi_t:\mathcal M \to \mathbb{E}\) and its
first jet extension \(\pi: J_1(\mathcal M) \to \mathcal M\) in a way that ensures total
compliance with coordinate and frame invariance requirements of
Classical Mechanics. We specify the differences between geometric
and constitutive characterizations of a constraint. We point out
the relevance of the role played by the concept of frame of
reference, underlining when the frame independence is mandatorily
required and when a choice of a frame is an inescapable need. The
thorough rationalization allows the introduction of unusual but
meaningful kinds of constraints, such as unilateral kinetic
constraints or breakable constraints, and of new theoretical
aspects, such as the possible dependence of the impulsive reaction
by the active forces acting on the system.
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