- #1
Reshma
- 749
- 6
The Lagrangian of a system is given by:
L = T - V, T = kinetic energy of the system, V = potential energy of the system.
L is a function of the generalised coordinates for a system of N particles given by:[tex] L = L(q_1, q_2, ...,q_{3N},\dot{q_1}, \dot{q_2},...,\dot{q_{3N}}, t)[/tex]
Suppose L is not an explicit function of a given coordinate qi then:
[tex]\frac{\partial L}{\partial q_i} = 0[/tex]
Such coordinates are the ignorable coordinates by definition. What if L is not an explicit function of time 't'? What is the nature of such a system where the Lagrangian is independent of time?
L = T - V, T = kinetic energy of the system, V = potential energy of the system.
L is a function of the generalised coordinates for a system of N particles given by:[tex] L = L(q_1, q_2, ...,q_{3N},\dot{q_1}, \dot{q_2},...,\dot{q_{3N}}, t)[/tex]
Suppose L is not an explicit function of a given coordinate qi then:
[tex]\frac{\partial L}{\partial q_i} = 0[/tex]
Such coordinates are the ignorable coordinates by definition. What if L is not an explicit function of time 't'? What is the nature of such a system where the Lagrangian is independent of time?