The principle of virtual work and Hamilton's principle on Galilean manifolds

Capobianco Giuseppe; Winandy Tom; Eugster Simon R.

doi:10.3934/jgm.2021002

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2021, Volume 13, Issue 2: 167-193. Doi: 10.3934/jgm.2021002

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The principle of virtual work and Hamilton's principle on Galilean manifolds

Institute for Nonlinear Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany

^* Corresponding author: Giuseppe Capobianco
^* Corresponding author: Giuseppe Capobianco

Received: March 2020

Revised: September 2020

Early access: January 2021

Published: June 2021

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Abstract

To describe time-dependent finite-dimensional mechanical systems, their generalized space-time is modeled as a Galilean manifold. On this basis, we present a geometric mechanical theory that unifies Lagrangian and Hamiltonian mechanics. Moreover, a general definition of force is given, such that the theory is capable of treating nonpotential forces acting on a mechanical system. Within this theory, we elaborate the interconnections between classical equations known from analytical mechanics such as the principle of virtual work, Lagrange's equations of the second kind, Hamilton's equations, Lagrange's central equation, Hamel's generalized central equation as well as Hamilton's principle.

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Mathematics Subject Classification: Primary: 70S05, 70H03, 70H05, 70H25; Secondary: 70A05, 53Z05.

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