Recent content by YogiBear

Homework Statement A chain of length L and uniform mass per unit length ρ is suspended in a uniform gravitational field. The potential energy U[y] and length l[y] functionals of the chain can be written in terms of y(x) as follows: U[y] = ρg*Int(y(1+y'^2)^1/2 dx) l[y] = Int((1+y'^2)^1/2)...

Thanks, I was actually able to solve that part using t = n(y)/A substitution. However now i have to do the following: "Determine the trajectory y(x) of a ray of light that just grazes the ground at x = xg as shown in the figure (i.e. determine expressions for A and x0 for this ray). Figure, in...

Mirage: we consider the x-y plane describing vertical y and horizontal x directions, with an inhomogeneous index of refraction n(y). In this case, using calculus of variations, Fermat’s principle for the trajectory of a ray of light may be re-written as n(y)/√1+(dy/dx)^2 = A. Where A is a real...

Thank you solved, it. <3

Homework Statement Let C be the straight line from the point r =^i to the point r = 2j - k Find a parametric form for C. And calculate the line integrals ∫cV*dr and ∫c*v x dr where v = xi-yk. and is a vector field Homework EquationsThe Attempt at a Solution For parametric form (1-t)i + (2*t)j...

Of course. I rushed to conclusion without reading question fully... thanks for the help thought, i would have had it completely wrong otherwise.

I have figured out part 2, very similar to part one. Cross multiply the matrix, and we get 0. I think I am getting somewhere on part three as well. Thank you. And your LaTeX skills are too good xD

Homework Statement The gradient, divergence and curl in spherical polar coordinates r, ∅, Ψ are nablaΨ = ∂Φ/∂r * er + ∂Φ/∂∅ * e∅ 1/r + ∂Φ/∂Ψ * eΨ * 1/(r*sin(∅)) nabla * a = 1/r * ∂/∂r(r2*ar) + 1/(r*sin(∅)*∂/∂∅[sin(∅)a∅] + 1/r*sin(∅) * ∂aΨ/∂Ψ nabla x a = |er r*e∅ r*sin(∅)*eΨ | |∂/∂r ∂/∂∅...