Titlebook: Classical and Quantum Dynamics; From Classical Paths Walter Dittrich,Martin Reuter Textbook 20013rd edition Springer-Verlag Berlin Heidelbe

PHAG

发现

阴郁

forthy

怒目而视

Blessing Mbipom,Susan Craw,Stewart MassieWe begin this chapter with the definition of the action functional as time integral over the Lagrangian ..., ... of a dynamical system:

chastise

Yichao Lu,Ruihai Dong,Barry SmythThe main purpose of this chapter is to consider the formulation of a relativistic point particle in classical electrodynamics from the viewpoint of Lagrangian mechanics. Here, the utility of Schwinger’s action principle is illustrated by employing three different kinds of action to derive the equations of motion and the associated surface terms.

clarify

D. J. H. Burden,M. Savin-Baden,R. BhaktaWe begin this chapter by deriving a few laws of nonconservation in mechanics. To this end we first consider the change of the action under rigid space translation δ.. = δε., and δ.(..) = 0. Then the noninvariant part of the action, . is given by . and thus it immediately follows for the variation of . that . or

cognizant

破裂

Hossein Ghodrati Noushahr,Samad AhmadiWe already know that canonical transformations are useful for solving mechanical problems. We now want to look for a canonical transformation that transforms the 2. coordinates (....) to 2. constant values (.., ..), e.g., to the 2. initial values (q., p.) at time . = 0. Then the problem would be solved, . = .(.., .., .), . = .(.., .., .).

我不明白

Animal Welfare Lessons from Work on Poultry,We shall first use an example to explain the concept of adiabatic invariance. Let us consider a “super ball” of mass ., which bounces back and forth between two walls (distance .) with velocity ... Let gravitation be neglected, and the collisions with the walls be elastic. If .. denotes the average force onto each wall, then we have