Title: The Equations of Motion for a System of Particles
Abstract:In this chapter, we establish Lagrange's equations for a system of particles by starting with the balances of linear momentum for each of the particles. Our derivation is based on the results presente...In this chapter, we establish Lagrange's equations for a system of particles by starting with the balances of linear momentum for each of the particles. Our derivation is based on the results presented in Chapter 15 of Synge and Griffith. We supplement their work with a discussion of constraints and potential energies. To examine the geometry inherent in Lagrange's equations of motion for the system of particles, we use the construction of a representative single particle by Casey. All the work presented in this chapter emphasizes the equivalence of Lagrange's equations of motion for a system of particles and the balances of linear momenta. For completeness, a brief discussion of the principle of virtual work, D'Alembert's principle, Gauss' principle of least constraint, and Hamilton's principle are also presented in Section 4.11. The chapter closes with a discussion of a canonical form of Lagrange's equations of motion in which time-independent integrable constraints are present.Read More
Publication Year: 2008
Publication Date: 2008-08-04
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot