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Lagrangians NOTnot of the form $T-U$

3 Dear ZAC, if u don't like my changes please roll back or use the parts u like.
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Lagrangian Lagrangians NOT of the form $ T$T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are aware of any such examples?

Update: Here I'm of course assuming that $T$ and $U$ stands for the kinetic and the potential energy, respectively. Also:

  1. adding a total time derivative term to the Lagrangian, or

  2. scaling the Lagrangian with a non-zero multiplicative constant

do not change the Euler-Lagrange equations, as Dilaton and dmckee points out in the comments. Needless to say that I'm not interested in such trivial modifications (1&2).

Lagrangian NOT of the form $ T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are aware of any such examples?

Lagrangians NOT of the form $T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are aware of any such examples?

Update: Here I'm of course assuming that $T$ and $U$ stands for the kinetic and the potential energy, respectively. Also:

  1. adding a total time derivative term to the Lagrangian, or

  2. scaling the Lagrangian with a non-zero multiplicative constant

do not change the Euler-Lagrange equations, as Dilaton and dmckee points out in the comments. Needless to say that I'm not interested in such trivial modifications (1&2).

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2 retagged; layout;
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Lagrangian NOT of the form $ T-UU$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy - Potential EnergyKinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. AreAre you are aware of any such examples?

Lagrangian NOT T-U

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy - Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are aware of any such examples?

Lagrangian NOT of the form $ T-U$

My Physics teacher was reluctant to define Lagrangian as Kinetic Energy minus Potential Energy because he said that there were cases where a system's Lagrangian did not take this form. Are you are aware of any such examples?

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