I have this question,
Express the length of a given curve r = r(\theta) in radial co-ordinates. Using the Variational principle derive the shortest path between two points is a line.
Ive drawn a picture with two angles (measured from the x-axis) \theta_1 and \theta_2 so that r(\theta_1) =...
I have another difficult question regarding calculus of variations.
A particle travels in the (x,y) plane has a speed u(y) that depends on the distance of the particle from the x-axis. The direction of travel subtends an angle \theta with the x-axis that can be controlled to give the minimum...
I am facing a difficult integral here for calculus of variations. The question reads:
Find the extremum to the integral:
I[y(x)] = \int_{Q}^{P} (dy/dx)^2(1+dy/dx)^2 dx
where P = (0,0) and Q = (1,2)
Hi all,
I seeking some advice about the calculus of variations.
I am an undergraduate and i am enrolled in a topic of the above mentioned. After successfully completing the requirments for the topic, 3 weeks after commencement i am feeling way out of my depth. I understand that the calculus...