Post by: jeffreyH on 21/12/2014 16:05:27
Post by: alancalverd on 21/12/2014 17:03:03
Post by: jeffreyH on 21/12/2014 17:42:47
They are both conserved. So when rigid gravitational masses move past each other, they will follow curved paths such that the total angular momentum and kinetic energy remain constant.
Thanks Alan. I need to do a bit more reading up on this but just wanted an initial response to confirm my initial thoughts.
Post by: PmbPhy on 21/12/2014 20:46:09
Quote from: jeffreyH
What is the relationship between kinetic energy and angular momentum?Jeff. Have you studied Lagrangian or Hamiltonian mechanics as of yet? If so then you'd have known the answer to this question. That's the benefit of studying various forms of mechanics.
You want a relationship between K and p, right?
p = mv
Q.E.D.
Post by: jeffreyH on 21/12/2014 21:28:13
Quote from: jeffreyHWhat is the relationship between kinetic energy and angular momentum?Jeff. Have you studied Lagrangian or Hamiltonian mechanics as of yet? If so then you'd have known the answer to this question. That's the benefit of studying various forms of mechanics.
You want a relationship between K and p, right?
p = mv
Q.E.D.
I have studied neither yet but I need to get round to that. Thanks for the equations they will be useful. Do you have any recommendations for textbooks on the above mentioned mechanics?
Post by: PmbPhy on 21/12/2014 21:57:58
Quote from: jeffreyH
I have studied neither yet but I need to get round to that. Thanks for the equations they will be useful. Do you have any recommendations for textbooks on the above mentioned mechanics?I'm happy to see that those relationship were what you had in mind!
The textbooks below are all very good and can be downloaded from the internet at the URLs I gave below the title for free. I'm sure you'll enjoy them. As always, I'm at your disposal. :)
The term Analytical Mechanics refers to the mechanics of Lagrangian and Hamiltonian Mechanics. See: http://en.wikipedia.org/wiki/Analytical_mechanics
One typically uses Variational principles in working with these areas of classical mechanics.
The Variational Principles of Mechanics by Cornelius Lanczos (1970) is famous for this branch of mechanics. It's quite well-known.
Newtonian Mechanics by A.P. French (1971) [Does not contain Analytical Mechanics]
http://bookzz.org/book/2033048/f8d850
An Introduction to Mechanics by Daniel Kleppner & Robert J. Kolenkow (1973) [Does not contain Analytical Mechanics]
(Not available online)
Classical Mechanics by John R. Taylor (2005)
http://bookzz.org/book/911552/c4bf66
Classical Dynamics of Particles and Systems by Marion and Thornton (2004)
http://bookzz.org/book/556792/ca7948
Solved Problems in Classical Mechanics; Analytical and numerical solutions with comments by O.L De Lange & J. Pierrus (2010)
Classical Mechanics by Haret C. Rosu
http://arxiv.org/abs/physics/9909035