In the solution of a pendulum attached to a wheel problem, I was initially suprised to see that a term of the form:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{df}{dt}

[/tex]

"can be removed from the Lagrangian since it will have no effect on the equations of motion".

ie: [itex]L' = L \pm df/dt[/itex] gives identical results.

f in this case was cos(\omega t + \theta) where theta was the generalized coordinate.

I confirmed this for the cosine function in this example by taking derivatives, and then confirmed that this is in fact a pretty general condition, given two conditions:

1) equality of mixed partials:

[tex]

\frac{\partial^2 f}{\partial t \partial q^i} = \frac{\partial^2 f}{\partial q^i \partial t}

[/tex]

2) no dependence on velocity coordinates for time partial derivative:

[tex]

\frac{\partial^2 f}{\partial \dot{q}^i \partial t} = 0

[/tex]

Does this ability to add/remove time derivatives of functions from the Lagrangian that aren't velocity dependent have a name?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lagrangian question. ability to remove time derivative terms.

**Physics Forums | Science Articles, Homework Help, Discussion**