Vol. 83 (2019) REPORTS ON MATHEMATICAL PHYSICS No. 3 A JET BUNDLE APPROACH TO THE VARIATIONAL STRUCTURE OF NONHOLONOMIC MECHANICAL SYSTEMS MAHDI KHAJEH SALEHANI * School of Mathematics, Statistics and Computer Science, College of Science, University of Tehran, P.O. Box: 14155-6455, Tehran, Iran (e-mail: salehani@ut.ac.ir) and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran (Received August 23, 2018 — Revised January 7, 2019) The aim of this paper is to study the geometry of nonholonomic mechanical systems in the realms of geometric mechanics and geometric analysis. This work was intended as an attempt at bringing together these two areas, in which geometric methods play the major role, in the study of nonholonomic systems. In this paper, we explore the geometry of Lagrangian mechanical systems subject to nonholonomic constraints using various bundle and variational structures intrinsically present in the nonholonomic setting. We consider the constrained Hamel equations of motion in a way that aids the analysis and helps to highlight the variational structure of such equations. To illustrate results of this work and as an application of the constrained Hamel formalism discussed in this paper, we conclude with taking the balanced Tennessee racer into consideration. Keywords: jet bundle, nonholonomic mechanical system, constrained Hamel formalism, varia- tional structure. 2010 Mathematics Subject Classification. Primary: 53C80, 70F25; Secondary: 70G45, 70G75. 1. Introduction Nonholonomic systems come in two varieties. On one hand, there exist those with dynamic nonholonomic constraints, i.e. constraints preserved by the basic Euler– Lagrange or Hamilton equations, such as angular momentum, or more generally momentum maps. In fact, these “constraints” are consequences of the equations of motion, and so it is sometimes convenient to treat them as conservation laws rather than constraints per se. On the other hand, kinematic nonholonomic constraints are those imposed by the kinematics, such as rolling constraints, which are constraints that are not derivable from position constraints [1]. * This work was supported in part by a grant from the Institute for Research in Fundamental Sciences (IPM) [No. 96510034]. [373]