Tagged Questions
1
vote
1answer
90 views
Classical Mechanics and the Hamiltonian
This problem has to do with a canonical transformation and Hamiltonian formalism. Below is my attempt at solving it, but I am not too sure about it. Please help!
Let $\theta$ be some parameter.
And
...
1
vote
2answers
87 views
replace a differential equation by an equivalent system of first order equations:
If a particle of mass $m$ moves in the $x$-$y$ plane, then its equations of motion are
$$m\frac{d^2x}{dt^2}=f(t,x,y)\space \space \text{and} \space \space m\frac{d^2y}{dt^2}=g(t,x,y).$$
Here $f$ ...
3
votes
0answers
118 views
system of implicit nonlinear differential equations
Here I have a system of nonlinear differential equations:
$
(M+2m)\ddot{x} + m(l_1 \ddot{\theta}_1\cos\theta_1 - l_1\dot{\theta}_1^2\sin\theta_1) + ...
0
votes
1answer
199 views
Find the derivative of $F =$ $(GmM)\over r^2$
Newton's Law of Gravitation says that the magnitude F of the force exerted by a body of mass M on a body of mass m is
$F =$ $(GmM)\over r^2$
Where G is the gravitational constant and r is the ...
12
votes
1answer
217 views
Is it possible to formulate variational calculus geometrically?
In textbooks I've seen differential geometry is done with finite-dimensional manifolds. Is it possible to generalise to banach manifolds so as to formulate the calculus of variations within it, or ...
5
votes
0answers
634 views
Restricted Three-Body Problem
The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...
