Does an infinitesimal generator of acceleration exist?

In summary, there is no such thing as a generator of acceleration, as acceleration cannot be a generalized coordinate in classical dynamics. However, it can appear in the formula for a generalized coordinate, multiplied by mass to get force. Additionally, the accelerations do not form a Lie group, making it impossible to have an infinitesimal generator for acceleration.
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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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1. What is an infinitesimal generator of acceleration?

An infinitesimal generator of acceleration is a hypothetical concept in physics that refers to a force or mechanism that is capable of producing infinitesimally small changes in an object's velocity. It is often used in the study of fluid dynamics and is closely related to the concept of turbulence.

2. How does an infinitesimal generator of acceleration differ from a regular force?

An infinitesimal generator of acceleration differs from a regular force in that it is capable of producing changes in an object's velocity that are extremely small and difficult to detect. Regular forces, on the other hand, can produce larger and more noticeable changes in an object's velocity.

3. Is there any evidence for the existence of an infinitesimal generator of acceleration?

Currently, there is no direct evidence for the existence of an infinitesimal generator of acceleration. However, its effects can be observed indirectly through the study of turbulence and other fluid dynamics phenomena.

4. How is the concept of an infinitesimal generator of acceleration useful in physics?

The concept of an infinitesimal generator of acceleration is useful in physics because it allows scientists to better understand and predict the behavior of fluids, which are notoriously difficult to study. It also helps to explain certain phenomena, such as turbulence, that cannot be fully described by regular forces.

5. Are there any practical applications for the concept of an infinitesimal generator of acceleration?

While there are no direct practical applications for the concept of an infinitesimal generator of acceleration, it has been used in various theoretical and computational models to better understand and predict the behavior of fluids. This can have implications in fields such as aerospace engineering, meteorology, and oceanography.

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