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A Does an infinitesimal generator of acceleration exist?

  1. Nov 17, 2016 #1
    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?
  2. jcsd
  3. Nov 17, 2016 #2
    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.
    Last edited: Nov 17, 2016
  4. Nov 18, 2016 #3


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  5. Nov 18, 2016 #4

    A. Neumaier

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    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.
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