From: pnachtwey@gmail.com   
      
   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])$   
      
   tlist: makelist(s[i][1],i,1,length(s))$   
   ulist: makelist(s[i][2],i,1,length(s))$   
   xlist: map(lambda([u],''x),ulist)$   
   ylist: map(lambda([u],''y),ulist)$   
   zlist: map(lambda([u],''z),ulist)$   
   wxplot2d([[discrete,tlist,xlist],[discrete,tlist,ylist],[discret   
   ,tlist,zlist]],   
           [legend,"x","y","z"],[xlabel,"time"],[ylabel,"Positions"]);   
      
   dudtlist: map(lambda([u],''dudt),ulist)$   
   dxdt: diff(x,u)*dudt$   
   dxdtlist: map(lambda([u],''dxdt),ulist)$   
   dydt: diff(y,u)*dudt$   
   dydtlist: map(lambda([u],''dydt),ulist)$   
   dzdt: diff(z,u)*dudt$   
   dzdtlist: map(lambda([u],''dzdt),ulist)$   
   speed: sqrt(dxdt^2+dydt^2+dzdt^2)$   
   speedlist: map(lambda([u],''speed),ulist)$   
   wxplot2d([[discrete,tlist,dudtlist],   
             [discrete,tlist,dxdtlist],   
             [discrete,tlist,dydtlist],   
             [discrete,tlist,dzdtlist],   
             [discrete,tlist,speedlist]],   
           [legend,"dudt","dxdt","dydt","dzdt","speed"],   
           [xlabel,"time"],[ylabel,"Speed"],['y,-1.1*v,1.1*v]);   
      
   BTW, I haven't been on the group for about 2 years.  I see the same people are   
   still here.   
      
   Thanks,   
      
   Peter   
      
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