Can time be a generalized coordinate?

[Visceral]

The title pretty much says it. According to my book, Classical Dynamics by Thornton and Marion, generalized coordinates can be quantities other than position such as energy or length squared, but what about time?

 

[A. Neumaier]

The title pretty much says it. According to my book, Classical Dynamics by Thornton and Marion, generalized coordinates can be quantities other than position such as energy or length squared, but what about time?

I guess, time is not a quantity in the sense of your book. It is the parameter parameterizing the dynamics.

 

[nlsherrill]

I guess, time is not a quantity in the sense of your book. It is the parameter parameterizing the dynamics.

I was just working on a problem the other day that had force as a function of position and time, and had to derive the potential and then the lagrangian and hamiltonian. So essentially, the answer is no?

 

[A. Neumaier]

I was just working on a problem the other day that had force as a function of position and time, and had to derive the potential and then the lagrangian and hamiltonian. So essentially, the answer is no?

The main stream view is indeed ''no''. But there is a trickle of literature (I don't remember precise references now) which works in extended pase spase where time and energy are anotherr pair of conjugate variables. However, this approach has its own pitfalls and is not widely used because of that.
Certainly it is not meant in your case unless your book explicitly discusses extended phase space.