This document is a brief overview of the Hamilton-Jacobi theory of Chaplygin systems based on [1]. In this paper, after reducing Chaplygin systems, Ohsawa et al. use a technique that they call Chaplygin Hamiltonization to turn the reduced Chaplygin systems into Hamiltonian systems. This method was first introduced in a paper by Chaplygin in 1911 where he reduced some nonholonomic systems by the...

This is the second paper in a series of works devoted to nonholonomic Ricci flows. By imposing non–integrable (nonholonomic) constraints on the Ricci flows of Riemannian metrics we can model mutual transforms of generalized Finsler–Lagrange and Riemann geometries. We verify some assertions made in the first partner paper and develop a formal scheme in which the geometric constructions with Ricc...

We present a new second order extension of the generalized-α method for systems in mechanics with a nonconstant mass matrix, holonomic constraints, and nonholonomic constraints. A new variable stepsizes formula preserving the second order of the method is also proposed.

This work considers a class of multibody dynamic systems involving bilateral nonholonomic constraints. An appropriate set equations motion is employed first. derived by application Newton’s second law and appears as coupled system strongly nonlinear second-order ordinary differential in both the generalized coordinates Lagrange multipliers associated with Next, these are manipulated properly co...

This paper develops a constructive method for finding a nilpotent basis for a special class of smooth nonholonomic distributions. The main tool is the use of the Goursat normal form theorem which arises in the study of exterior differential systems. The results are applied to the problem of finding a set of nilpotent input vector fields for a nonholonomic control system, which can then used to ...