# Question:Numerical Integration in Phase Space of ODE Solutions

## Question:Numerical Integration in Phase Space of ODE Solutions

Maple
Hello all, I am still quite new to Maple and this website, and apologize if this is an easy task or one that has been already addressed on the forums. I am trying to calculate an adiabatic invariant for a particle orbit. This invariant is the action over one oscillation in the particle's trajectory, and requires me to numerically integrate aspects of the plot in phase space. I calculated and plotted the particle's trajectory in phase space using the dsolve and odeplot commands. The invariant is given by the expression \int_{1 cycle} rho' drho where rho is the radial component of the particle trajectory as a function of time. Is there a command which I can use to perform this integration? Thanks for your help, Phil
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