Can someone help me with this exercise?
The material point M (m=1) in the Oxy plane moves on the effect of a force field which components are $F_{x}=y$,$F_{y}=x$.
- Is there a power function and if so, determine it!
- Determine the mechanical force performed by the above force along a straight line of equation y = x between points A(1, 1) and B(2, 2)!
- Determine the energy constant if the point of mass from point A (1, 1) with velocity $v_{0}=(1, 3)$ starts moving!
- Prove that the moving point started with the initial conditions given at the previous point due to the force can never get to point C (2, −3)!
- How long does it take (t=?) for the point of mass due to the given force to reach the point B(2,2) from point A(1,1) at the initial velocity $v_{0}=(1, 1)$?
For the first question there is for sure a power function because $\frac{dF_{x}}{dy}=\frac{dF_{y}}{dx}$ ,(1=1) and i tried to determine it using this equation and i got $U(x,y)=xy-x_{0}y_{0}$ but how can i get rid of $x_{0},y_{0}$?
For the next question i used this equation and i got that L=3. For the third question i got that the energy constant is h=$x_{0}y_{0}$+4 using this equation knowing that V=-U.I dont know how to solve the next two questions and im not sure if my previous results are correct?
