How Does Goldstein Derive the Kinetic Energy Equation in Classical Mechanics?

[bengeof]

how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 )

Thank You

 

[PeroK]

how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 )

Thank You

Chain rule.

 

[bengeof]

Can you work it out for me explicitly ?

 

[Ibix]

Can you state the chain rule? Can you apply it to the time derivative of $(dr/dt)^2$?

 

[PeroK]

Can you work it out for me explicitly ?

https://physics.stackexchange.com/questions/191826/derivative-of-kinetic-energy

 

[bengeof]

Can you state the chain rule? Can you apply it to the time derivative of $(dr/dt)^2$?

2dr/dt . . is that right ?

 

[bengeof]

https://physics.stackexchange.com/questions/191826/derivative-of-kinetic-energy

I was able to work out the right hand side. But the left hand side is my problem. .

 

[PeroK]

I was able to work out the right hand side. But the left hand side is my problem. .

That makes no sense. The LHS is the answer to the derivative on the RHS. There's nothing to work out on the left.

2dr/dt . . is that right ?

The stackexchange link I gave you is all about why that is not the answer!

 

[bengeof]

okay Got it. Thank you so much !

 

[Dr.D]

The rest of Goldstein may present difficulties.