It's been too long since I have done differential equations and I am not sure the best tools to solve this problem.
I am starting with a basic kinematic equation for the balance of forces.
P\v - ((A*Cw*Rho*v^2)/2 + m*g*Crl + m*g*slope) = m*a
P: power
x: position
v: velocity, x'
a: acceleration x"
(A*Cw*Rho*v^2)/2 : air resistance
m*g*Crl : rolling resistance
m*g*slope : potential energy (elevation)
I am modifying the above equation so that air velocity and slope are dependant on location x.
Vair = v + f(x) where f(x) is the weather component and a function of location x.
Same goes for slope, slope = g(x)
Power is a function I what to optimize/find to minimize time but at this time just simulate. maybe something like:
P = 2500/(v+1)
I will have restriction on P but not interested in that now.
The "course" I what to simulate therefore defines slope and wind speed. and is of a fixed distance.
I have played with some of the simple scipy.integrate.odeint examples. I get that I need to define a system of equations but am not really sure the rules for doing so. A little help would be greatly appreciated.