This chapter develops differential forms and the exterior derivative, then applies them to integrability, thermodynamics and classical mechanics.
Contents
- 16.1 Differential forms and exterior derivative
- 16.2 Properties of exterior derivative
- 16.3 Frobenius theorem: dual form
- 16.4 Thermodynamics
- 16.5 Classical mechanics
Concept index
Terms by section. Links lead to the brown underlined definitions in the Chinese reading text.
16.1 Differential forms and exterior derivative
16.3 Frobenius theorem: dual form
16.4 Thermodynamics
- equilibrium state平衡态
- quasi-static process准静态过程
- reversible process可逆过程
- adiabatic enclosure绝热围壁
- adiabatic process绝热过程
- empirical temperature经验温度
- isotherm等温线
- internal energy内能
- work form功形式
- empirical entropy经验熵
- absolute temperature绝对温度
- absolute entropy绝对熵
16.5 Classical mechanics
- Lagrangian function拉格朗日函数
- action作用量
- Euler–Lagrange equations欧拉–拉格朗日方程
- generalized coordinate广义坐标
- Riemannian manifold黎曼流形
- configuration space位形空间
- generalized momentum广义动量
- cyclic coordinate循环坐标
- symplectic structure辛结构
- symplectic manifold辛流形
- Hamiltonian vector field哈密顿向量场
- dynamical variable动力学变量
- phase space相空间
- homogeneous contact transformation齐次接触变换
- contact transformation接触变换
- Hamilton–Jacobi equation哈密顿–雅可比方程