An object moves in 3 dimensions so the magnitude of the velocity is v=sqrt(diff(x,u)^2+diff(y,u)^2+diff(z,u)^2); Now I want u to be a function of time, u(t) and compute u(t) symbolically so that the velocity is a constant v. I can find the solution if I use RK but that doesn't get me the symbolic solution. Am I expecting too much from wxMaxima? Maybe I am not using the integrate function right but the iterative RK solution works. At this time I am trying to do some of this manually the hard way.
Here is my RK solution and graphs the I have in 3 wxMaxima cells. You should be able to cut and paste to see what I am trying to do. In actual use x(u),y(u) and z(u) are probably going to be 3rd or 5th order polynomials.
remvalue(all)$ v: 1$ /* The constant speed to maintain */ x: 1*sin(u)$ /* x as a function of u */ y: 1*sin(u+2*%pi/3)$ /* y as a function of u */ z: 2*sin(0.5*u+2*%pi/3)$ /* z as a function of u */ 'diff(u,t)=dudt: v/sqrt(diff(x,u)^2+diff(y,u)^2+diff(z,u)^2); s: rk(dudt,u,0,[t,0,10,0.01])$