Does an infinitesimal generator of acceleration exist?

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Discussion Overview

The discussion centers around the existence of an infinitesimal generator of acceleration within the context of field theories and Lagrangian mechanics. Participants explore the implications of acceleration as a generalized coordinate and its relation to transformations in theoretical physics.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions whether an infinitesimal generator of acceleration exists and seeks guidance on constructing a related matrix.
  • Another participant asserts that there is no generator of acceleration, stating that acceleration cannot be treated as a generalized coordinate, but can appear in the context of force.
  • A third participant references a specific thesis to provide additional context related to Newtonian gravity, suggesting it may be relevant to the discussion.
  • A later reply challenges the notion of acceleration forming a Lie group, indicating that this is necessary for discussing infinitesimal generators, and contrasts it with generators for translations and rotations.

Areas of Agreement / Disagreement

Participants express differing views on the existence of an infinitesimal generator of acceleration, with no consensus reached on the matter. Some argue against its existence while others explore the concept further.

Contextual Notes

Participants note that the lack of a Lie group structure for accelerations complicates the discussion of infinitesimal generators. There are also references to specific theoretical frameworks and principles that may not be universally accepted or understood.

quickAndLucky
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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?
 
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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.
 
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quickAndLucky said:
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.
 
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