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I am trying to set up a code to calculate the equation of motion of a rocket using ode45

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Jose Camorlinga Medina
评论： Jose Camorlinga Medina 2018-10-8
My equation for the EOM are
dv/dt= T/m - D/m - g*sin(gam): at=tangential acceleration, T=thrust, D=drag, g=acceleration of gravity, gam= path angle
dgam/dt= -1/v*(g-(v^2/(Re+h)))*cos(gam): v=velocity, Re=radius of earth, h= altitude
dx/dt=Re/(Re+h)*v*cos(gam): x is downrange distance
dh/dt=v*sin(gam):
I have been watching videos, but I am not sure how to use ode45 with multiple functions, I would appreciate the help.
  2 个评论
Torsten
Torsten 2018-10-8
Name v=y(1), gam=y(2), x=y(3) and h=y(4) and set up the ODE system for ODE45 like in the examples of the documentation.
Jose Camorlinga Medina
Jose Camorlinga Medina 2018-10-8
I was trying to follow that example, this is what I have so far
function dy = trajectory(t,y)
dy = zeros(4,1);
mf = mo-mpi; % Mass after propellent runs out (kg)
n = mo/mf; % Initial to final mass ratio ()
% time
t0 = 0; % Initial time (s)
tb = mf/md; % Burnout time (s)
tf = tb;
tspan = [t0,tf];
% Initial condition
v0 = 0; % Initial velocity (m/s)
gamma0 = 89.85*deg; % Initial flight path angle (rad)
x0 = 0; % Initial downrange distance (km)
h0 = 0; % Initial altitude (km)
vD0 = 0; % Initial value of velocity loss due to drag (m/s)
vG0 = 0; % Initial value of velocity loss due to gravity (m/s)
f0 = [v0; gamma0; x0; h0; vD0; vG0]; % Initial condition vector
% Equations of motion
dy(1) = (Ftv/m)-(D/m)-g*sin(y(2)); % Acceleration along path (m/s^2)
dy(2) = -(1/y(1))*(g-(y(1)^2/(Re+y(4))))*cos(y(2)); % Rate of change of path angle (rad)
dy(3) = Re/(Re+y(4))*y(1)*cos(y(2)); % Downrange distance (m)
dy(4) = y(1)*sin(y(2)); % Altitude (m)
[t,y] = ode45('trajectoty',tspan,f0)

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