Matlab ode45 how to#

Options = odeset('MaxStep', 5) % Set maximum step size as 5 seconds

% Determine Orbital Period, this is just to determine how long to simulate for NOTE: Any variable referenced by an anonymous function that is not an input to the function, must be define before the function within the code. For this problem, anonymous functions are an excellent choice to code the state-space equation. Anonymous functions are convenient since they can be written within another script of function, but they can only contain one executable statement. Now LetвЂ™s Get StartedДЇor this problem, the equation of motion for the satellite will be coded as an anonymous function. To understand the input parameters for the ode45 function, type вЂњdoc ode45вЂќ and вЂњdoc odesetвЂќ in the MATLAB command window. The ode45 function within MATLAB uses the Dormand-Prince formulation. I recommend that students write their own Runge-Kutta function to better understand this algorithm prior to adopting that MATLAB internal function. For this problem, we will use the ode45 solver which uses a Runge-Kutta iterative method to achieve 4 th and 5 th order accuracy. The selection of the appropriate solver is dependent on the type of ODE you are solving and the desired accuracy. MATLAB has many ODE solvers available for the coder. The state-space representation of this equation becomes: Where Ој is the gravitational parameter of earth (398600 km 3/s 2)

Matlab ode45 how to#

For this tutorial, I will demonstrate how to use the ordinary differential equation solvers within MATLAB to numerically solve the equations of motion for a satellite orbiting Earth.ДЇor two-body orbital mechanics, the equation of motion for an orbiting object relative to a much heavier central body is modeled as: