On the History of the Development of the Nonholonomic Dynamics

TL;DR

This paper reviews the historical development of nonholonomic dynamics, highlighting formalism, problem analysis, and the role of computer-aided methods in advancing the field.

Contribution

It provides a concise overview of the main directions in nonholonomic dynamics development, emphasizing formalism, problem analysis, and computational approaches.

Findings

Different formalisms of nonholonomic equations are discussed.

Analysis of specific nonholonomic problems is emphasized.

Modern computer-aided methods are identified as promising for future research.

Abstract

The main directions in the development of the nonholonomic dynamics are briefly considered in this paper. The first direction is connected with the general formalizm of the equations of dynamics that differs from the Lagrangian and Hamiltonian methods of the equations of motion's construction. The second direction, substantially more important for dynamics, includes investigations concerning the analysis of the specific nonholonomic problems. We also point out rather promising direction in development of nonholonomic systems that is connected with intensive use of the modern computer-aided methods.