The Four Variational Principles of Mechanics

摘要: We argue that there are {ital four} basic forms of the variational principles mechanics: Hamilton{close_quote}s least action principle (HP), generalized Maupertuis (MP), and their two reciprocal principles, RHP RMP. This set is invariant under reciprocity Legendre transformations. One these (HP) in literature: only special cases other three known. The MP has a weaker constraint compared to traditional formulation, mean energy {bar E}} kept fixed between virtual paths. reformulation alleviates several weaknesses old version. (RMP) classical limit Schr{umlt o}dinger{close_quote}s quantum mechanics, this connection emphasizes importance transformation for principles. Two unconstrained formulations (UHP UMP) four also proposed, with completely specified Lagrange multipliers Percival{close_quote}s tori scattering orbits derived from RMP very convenient approximate solutions problems mechanics using Ritz type methods Examples provided. Copyright {copyright} 1996 Academic Press, Inc.