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A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena. (English) Zbl 1367.70037
Summary: A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe, in a unified way, other phenomena including friction, non-holonomic constraints and energy radiation (Lorentz-Abraham-Dirac force equation). A quantization rule adapted to the dissipative degrees of freedom is proposed which does not pass through the variational formulation.

70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
37J60 Nonholonomic dynamical systems
70F40 Problems involving a system of particles with friction
Full Text: DOI arXiv
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