Exploring Newton's Equations of Motion in Different Coordinate Systems

[M. next]

What are the Newton's equations of motion of a single particle (using cartesian, cylindrical, and spherical coordinates)?

I know the first: F=ma (Along x, y, z) But the in other coordinates?

 

[Ken G]

If you learn about "vectors", you will find that F=ma, written in vector form, is the correct expression for the law in any of those coordinates. You end up just needing to know how to express the components of F and a (the two vectors there) in those different coordinate systems, which is kind of a detail-- it sounds like you really only want the law, and the point of vectors is to able to write the law in just one way. One-stop shopping! The forms for the components in the different coordinates is probably best to just look up, I'll bet a google with the appropriate words would succeed easily. (F is easy, if you understand the coordinates, but a is a bit trickier.)

 

[M. next]

I just need the last form, the final one, so I can see if I reached the same form using Hamilton's Equation. I googled before posting this, I got nothing.

 

[Ken G]

Well, all I did was google "acceleration in spherical coordinates", and the first hit was http://www.csupomona.edu/~ajm/materials/delsph.pdf , so if you scroll down to "velocity and acceleration" you find the general form for acceleration in spherical coordinates. Then just match up the force components (radial, latitudinal, longitudinal) which should be easy enough if you know what force you are dealing with, and you have F=ma in component form in spherical coordinates.

 

[M. next]

Thank you Ken G.