How to numerically integrate the planar equations of motion?

For example, i have this equation for deacceleration

Written in MATLAB as dV/dt = -(rho*V^2)/(2*B) - g0*sin(gamma)

B (constant), rho, and gamma are all defined variables.

I am trying to use ode45, but can not get this to be a valid funtion to even use ode45. Below is my input and error I am getting.

dVdt = @(t,V), -(rho*V^2)/(2*B) - g0*sin(gamma)

Error: Invalid expression. Check for missing or extra characters

Any suggetions on how to approch this problem correctly would be greatly apprciated.

Answer 1

[John D'Errico]

You need to learn how to write a function handle. What you wrote was incorrect syntax. Do you see the spare comma, AFTER the parens?

dVdt = @(t,V), -(rho*V^2)/(2*B) - g0*sin(gamma)

Instead, this next is valid MATLAB syntax:

dVdt = @(t,V) -(rho*V^2)/(2*B) - g0*sin(gamma);

I added a semi-colon at the end. Learn to do that, although it is not crucial. The semi-colon stops lots of crap being dumped to your command widow.

[TKR]

thank you! i was missing the ; just trying to get it to work.

big question now is to how to get it to work in ODE45

Answer 2

[Torsten]

syms V(t) a1 a2
sol = dsolve(diff(V,t)==a1*V^2+a2)

sol = 

Now substitute a1 = -rho/(2*beta) and a2 = -g0*sin(gamma)