- #1
Trying2Learn
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This question concerns inertial frames.
I am aware that an inertial frame is one that is not accelerating.
I am aware of an alternative definition: it is one on which no forces are applied.
(Yes, they are the same thing.)
I am also aware of the d'Alembert "forces" that appear when a frame is not inertial.
And I have been satisfied with this for some time.
However, now I am hoping for a more mathematical definition of an inertial frame (but I admit I may be on the verge of confusing myself with an irrelevant issue).
First, go here to the Introduction of Frankel's text on the Geometry of Physics
http://assets.cambridge.org/97811076/02601/frontmatter/9781107602601_frontmatter.pdf
And go to the very last page.
There... right there he asserts that a basis can be obtained by unitized derivatives of the coordinate functions.
(I wish I could post the very next page, but you can get the idea).
I like that...
Now I am wondering if I can extend this to a definition of an inertial frame when the frame bases are obtained by partial derivatives of the coordinate functions that are parameterized by time.
I can sort of reason it for the case of rotations.
But could someone explain how to assert that a frame that is "accelerating in a straight line is not inertial," by using the notion of a frame derived from coordinate functions.
I am aware that an inertial frame is one that is not accelerating.
I am aware of an alternative definition: it is one on which no forces are applied.
(Yes, they are the same thing.)
I am also aware of the d'Alembert "forces" that appear when a frame is not inertial.
And I have been satisfied with this for some time.
However, now I am hoping for a more mathematical definition of an inertial frame (but I admit I may be on the verge of confusing myself with an irrelevant issue).
First, go here to the Introduction of Frankel's text on the Geometry of Physics
http://assets.cambridge.org/97811076/02601/frontmatter/9781107602601_frontmatter.pdf
And go to the very last page.
There... right there he asserts that a basis can be obtained by unitized derivatives of the coordinate functions.
(I wish I could post the very next page, but you can get the idea).
I like that...
Now I am wondering if I can extend this to a definition of an inertial frame when the frame bases are obtained by partial derivatives of the coordinate functions that are parameterized by time.
I can sort of reason it for the case of rotations.
But could someone explain how to assert that a frame that is "accelerating in a straight line is not inertial," by using the notion of a frame derived from coordinate functions.