- #1
Herbststurm
- 30
- 0
Hello
Maybe I am standing on a garden hose (great German adage, does it exist in english or are you confused what I am talking about?)
Okay, to the topic:
Just for one dimension. It is easier:
We have [tex] m\ddot{x} = F(x(t)) [/tex] Now my book tells me that if I expansion with the velocity I should get:
[tex] \frac{m}{2} \frac{d}{dt} \dot{x}^{2} = - \frac{d}{dt} U(x(t)) [/tex]
I don't understand. Sadly I learnet it a year ago and I forgot everything. How sad a fate! :-(
I understand the right-hand side. Force is the derivative of the potential, the field must be conservative. But I don't understand the left-hand side.
1.) why is there a two under the mass?
2.) I expansion with the velocity? the differentialoperator on the velocity is my acceleration and the second velocity is one from the expansion. Where is the second? I could only identify one velocity. What happend?
Thanks
greetings
Maybe I am standing on a garden hose (great German adage, does it exist in english or are you confused what I am talking about?)
Okay, to the topic:
Just for one dimension. It is easier:
We have [tex] m\ddot{x} = F(x(t)) [/tex] Now my book tells me that if I expansion with the velocity I should get:
[tex] \frac{m}{2} \frac{d}{dt} \dot{x}^{2} = - \frac{d}{dt} U(x(t)) [/tex]
I don't understand. Sadly I learnet it a year ago and I forgot everything. How sad a fate! :-(
I understand the right-hand side. Force is the derivative of the potential, the field must be conservative. But I don't understand the left-hand side.
1.) why is there a two under the mass?
2.) I expansion with the velocity? the differentialoperator on the velocity is my acceleration and the second velocity is one from the expansion. Where is the second? I could only identify one velocity. What happend?
Thanks
greetings