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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.

MSC:
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
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