# [Numpy-discussion] ODE how to?

Vincent Davis vincent at vincentdavis.net
Mon Oct 27 12:49:40 EDT 2014

```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.

Vincent Davis
720-301-3003
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