“Lagrange’s equations”的概念、定义、翻译、参考文献-科学参考

Lagrange’s equations

Mathematics

单词	Lagrange’s equations
释义	Lagrange’s equations Mathematics 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, $L = \frac{1}{2} m l^{2} {\dot{θ}}^{2} + m g l cos θ .$ For such a system, defined by generalized coordinates q₁, q₂, …, q_n, Lagrange’s equations state that $\frac{d}{d t} (\frac{\partial L}{\partial {\dot{q}}_{i}}) - \frac{\partial L}{\partial q_{i}} = 0 for 1 \leq i \leq n .$ In the example of the pendulum, this gives $0 = \frac{d}{d t} (m l^{2} \dot{θ}) + m g l sin θ = m l^{2} \ddot{θ} + m g l sin θ .$ See also Hamiltonian mechanics.
随便看	British Geological Survey British Honduras British Household Panel Survey British Interplanetary Society British National Space Centre British North America Act (1867) British Raj British Standards Institute British thermal unit British thermal unit per hour brittle brittle behaviour brittle star Brix broadband broadband antenna broadband coaxial systems broadband dipole broadband ISDN broadband networking broad-band photometry broadcast domain broadcasting broadcast quality video broadcast storm