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## Main Question or Discussion Point

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 q

[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 q

_{i}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?