- #1
NeutronStar
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I'm studying Lagrangian Dynamics using a Schaum's Outline. This book seems to assume that the student can easily set up the Differential Equations of motion, but I can't seem to get the hang of it. The book does not give any actual methods or examples for setting up these Differential equations of motion, they seem to be more concerned with just solving the resulting differential equations.
At the other extreme most of my classical physics books just give the standard equations of motion without really getting into calculus.
Are their any books out there that focus on just setting up the differential equations for a particlar mechanical system.
As an example there is a very simple problem in the Langrangian Dynamics book of a pendulum and spring system. (just one mass hanging from a spring allowed to move in the x-y plane only. It seems simple enough and they give the equations of motion as follows.
[tex] \ddot{r} - r \dot{\theta}^2 - g \cos \theta + \frac {k} {m} \left( r - r_o \right) = 0 [/tex]
and
[tex] r \ddot {\theta} + 2 \dot {r} \dot {\theta} + g \sin \theta = 0 [/tex]
I'd like to find a book that shows methodological procedures for arriving at these types of differential equations from the standard classical physics equations.
Any suggestions?
Also if someone feels like taking the time to show how the above equations where formed from the basic equations of a spring and pendulum motion that would be cool too.
Thank you.
At the other extreme most of my classical physics books just give the standard equations of motion without really getting into calculus.
Are their any books out there that focus on just setting up the differential equations for a particlar mechanical system.
As an example there is a very simple problem in the Langrangian Dynamics book of a pendulum and spring system. (just one mass hanging from a spring allowed to move in the x-y plane only. It seems simple enough and they give the equations of motion as follows.
[tex] \ddot{r} - r \dot{\theta}^2 - g \cos \theta + \frac {k} {m} \left( r - r_o \right) = 0 [/tex]
and
[tex] r \ddot {\theta} + 2 \dot {r} \dot {\theta} + g \sin \theta = 0 [/tex]
I'd like to find a book that shows methodological procedures for arriving at these types of differential equations from the standard classical physics equations.
Any suggestions?
Also if someone feels like taking the time to show how the above equations where formed from the basic equations of a spring and pendulum motion that would be cool too.
Thank you.
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