- #1
strokebow
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I am intending to use Runge Kutta 4th order to numerically solve a system of coupled equations:
[itex]\frac{d^{2}x}{dt^{2}}[/itex] = K1 * x * cos(t) + ( (K2 * [itex]\frac{dy}{dt}[/itex]) - [itex]\frac{dz}{dt}[/itex] )
[itex]\frac{d^{2}y}{dt^{2}}[/itex]= -K1 * y * cos(t) + ( (K2 * [itex]\frac{dz}{dt}[/itex]) - [itex]\frac{dx}{dt}[/itex] )
[itex]\frac{d^{2}z}{dt^{2}}[/itex]= ( (K2 * [itex]\frac{dx}{dt}[/itex]) - [itex]\frac{dy}{dt}[/itex] )
I'm really a bit stuck to be honest. I've only ever used RK4 on 1st order linear ODEs. I've been reading around a lot but not making much progress.
Initial values for [itex]\frac{dx}{dt}[/itex], [itex]\frac{dy}{dt}[/itex], [itex]\frac{dz}{dt}[/itex] are all known. The constants K are known.
Can anyone please help? Thanks
[itex]\frac{d^{2}x}{dt^{2}}[/itex] = K1 * x * cos(t) + ( (K2 * [itex]\frac{dy}{dt}[/itex]) - [itex]\frac{dz}{dt}[/itex] )
[itex]\frac{d^{2}y}{dt^{2}}[/itex]= -K1 * y * cos(t) + ( (K2 * [itex]\frac{dz}{dt}[/itex]) - [itex]\frac{dx}{dt}[/itex] )
[itex]\frac{d^{2}z}{dt^{2}}[/itex]= ( (K2 * [itex]\frac{dx}{dt}[/itex]) - [itex]\frac{dy}{dt}[/itex] )
I'm really a bit stuck to be honest. I've only ever used RK4 on 1st order linear ODEs. I've been reading around a lot but not making much progress.
Initial values for [itex]\frac{dx}{dt}[/itex], [itex]\frac{dy}{dt}[/itex], [itex]\frac{dz}{dt}[/itex] are all known. The constants K are known.
Can anyone please help? Thanks