Particle Kinetics using ODE45

please help me this problem. I have to solve this using ODE45 function.

[David Goodmanson]

Hi Wendy,

before you try to solve this (where you would use a vector with four components, the quantities shown in 2) in the problem statement), you should check with someone to see if these equations are even correct. I get (using prime instead of dot)

theta'' = 2 tan(phi) phi' theta'                         % agrees
phi'' = -sin(phi) cos(phi) (theta')^2 + (g/L) cos(phi)   % does not agree at all

I think part of the problem here is their strange use of phi as coming down from the xy plane rather than up from the negative z axis which is the usual choice.

[Bjorn Gustavsson]

@Wendy Chun, one clever thing to do when deriving these equations of motion is to test that they simlpify nicely. Here you could for example check that everything works OK if you give the particle-mass zero initial velocity at some [theta_0,phi_0]. Then (to my understanding) you should have a very ordinary particle pendulum - for which you (surely?) should have a solution already. Then you can test that your extended equations at least simplify to what you already know.