Here is a text that presents classical dynamics from a modern geometrical viewpoint, uniting this new perspective with the totality of knowledge in the field and introducing mathematical techniques
gradually as the reader studies the standard topics. The concepts of differential geometry are developed as a calculation tool, with emphasis on applications and not rigor. While $IDynamics$I treats traditional topics
in a general way, it frequently adds a nontraditional approach through the new geometrical method, for instance, recent developments in the variance of mechanical systems under perturbation and Lie algebra techniques
are introduced for the first time in any textbook. Topics covered include phase flows, Lagrangian dynamics, rigid bodies, small oscillations, invariants, Hamiltonian dynamics on the cotangent bundle, dynamics on phase
space, action-angle variables, and invariant tori. |
