Does an infinitesimal generator of acceleration exist?

[quickAndLucky]

I am trying to determine what types of field theories have a Lagrangian that is symmetric under an Infinitesimal acceleration coordinate transformations.

Does an infinitesimal generator of acceleration exist?

How could I go about constructing this matrix?

 

[secur]

No, there's no such thing as a generator of acceleration. In classical dynamics, acceleration can't be a generalized coordinate. But it can appear in the formula for a generalized coordinate, multiplied by mass to get force. AFAIK. Google "deriving equations of motion from D'Alembert's principle" for some relevant information.

 

[haushofer]

See section 3.5, page 51 of

http://www.rug.nl/research/portal/files/34926446/Complete_thesis.pdf

in the context of Newtonian gravity. Hope this helps :)

 

[A. Neumaier]

Does an infinitesimal generator of acceleration exist?

It is better to be thorough an lucky than to be quick and sloppy.

What do you mean by this? It sounds meaningless to me!

The accelerations do not form a Lie group, but the latter is a prerequisite for talking about infinitesimal generators. For example, there is an infinitesimal generator for translations, given by the momentum operator, and for rotations, given by angular momentum.