Block, SkipCaptcha, Automoderated users, Bots, edit
57,719
edits
Changes
Jump to navigation
Jump to search
Line 8:
Line 8: − ===Example===+ Line 31:
Line 31: − +
→Example: clean up & uniformity
L, the [[Lagrangian]] function, is defined as L = T - V, where T is the total kinetic energy of the system and V is the total potential energy of the system, q is the generalized coordinate, and Q is the generalized force. <math>{\partial L }/ {\partial \dot q}</math> is known as the generalized momentum.
L, the [[Lagrangian]] function, is defined as L = T - V, where T is the total kinetic energy of the system and V is the total potential energy of the system, q is the generalized coordinate, and Q is the generalized force. <math>{\partial L }/ {\partial \dot q}</math> is known as the generalized momentum.
==Example==
Consider a mass m attached a spring with spring constant k. The system has a single degree of freedom: x, the displacement of the mass from its equilibrium position. Then,
Consider a mass m attached a spring with spring constant k. The system has a single degree of freedom: x, the displacement of the mass from its equilibrium position. Then,
which is the same as the result one arrives at by just considering the forces acting on the mass in Newtonian mechanics.
which is the same as the result one arrives at by just considering the forces acting on the mass in Newtonian mechanics.
[[category:physics]]
[[Category:Physics]]