“Lagrange's equations”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lagrange's equations

释义

Lagrange's equations

For a mechanical system with n degrees of freedom in which conservative forces act and all constraints are holonomic, the Lagrangian is L = T−V, where T denotes kinetic energy and V denotes potential energy. For a light pendulum of length l with a mass m at the end and making an angle θ with the downward vertical,

For such a system, defined by generalized coordinates q1, q2, …, qn, Lagrange's equations state that

In the example of the pendulum, this gives