Premium
A geometric view on the kinematics of finite‐dimensional mechanical systems
Author(s) -
Winandy Tom,
Capobianco Giuseppe,
Eugster Simon R.
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800221
Subject(s) - mathematics , euler equations , mechanical system , equations of motion , kinematics , tangent bundle , tangent , context (archaeology) , simultaneous equations , mathematical analysis , manifold (fluid mechanics) , work (physics) , classical mechanics , geometry , differential equation , tangent space , computer science , physics , mechanical engineering , paleontology , artificial intelligence , engineering , biology , thermodynamics
Finite‐dimensional mechanical systems can be described in terms of a set of generalized coordinates and their time‐derivatives. In this case, the Lagrange equations of the second kind provide the equations of motion of these systems. The Volterra–Hamel–Boltzmann equations generalize the Lagrange equations of the second kind in the sense that they allow for more general velocity parametrizations. In this work, we show in the context of scleronomous finite‐dimensional mechanical systems that both sets of equations can be interpreted as being different chart representations of the intrinsic Euler–Lagrange equations on the tangent bundle over the configuration manifold of the mechanical system.