"There is some freedom as to what we choose for the Lagrangian in a given problem: We can add a constant, multiply by a constant, change the time scale by a multiplicative constant, or add the total time derivative ........... Any of these transformations will lead to a Lagrangian that is perfectly satisfactory for describing the motion."(adsbygoogle = window.adsbygoogle || []).push({});

I could not verify the 3rd one. Why is it possible to change the time scale by a constant factor?

For example:

[tex]L = \frac{1}{2}m\dot{q}^2 - kqt[/tex]

The E-L equation is

[tex]m\ddot{q} + kt = 0[/tex]

If we modify the Lagrangian, multiplying all time by constant c

[tex]L = \frac{1}{2c^2}m\dot{q}^2 - ckqt[/tex]

The E-L equation is

[tex]m\ddot{q} + c^3kt = 0[/tex]

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# Question on Lagrangian Mechanics

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