twobodyEOM: % ~~~~~~~~~~~~~~~~~~~~~~~~ function dYdt = twobodyEOM2D(t,Y,mu) % --

Question

twobodyEOM:

% ~~~~~~~~~~~~~~~~~~~~~~~~
function dYdt = twobodyEOM2D(t,Y,mu)
% ------------------------
%{
This function calculates first and second time derivatives of r
governed by the equation of two-body 2D motion

Y - column vector containing r and v at time t
dYdt - column vector containing drdt and dvdt at time t

User M-functions required: none
%}
% ~~~~~~~~~~~~~~~~~~~~~~~~

rvec = Y(1:2);
vvec = Y(3:4);

r = sqrt(rvec(1)^2+rvec(2)^2) ;

rdotvec = vvec ;
vdotvec = -mu/r^3*rvec ;

dYdt = [rdotvec; vdotvec];
end

CALLTWOBODY:

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% Example_1_20
% ~~~~~~~~~~~~~~~~~~~
%{
This program uses ode45 with adaptive step size control
to solve the 2D equations of motion of two-body motion
  
User subfunction required: twobodyEOM2D
%}
% ---------------------------------------------------------------------

clear all
close all
clc

% Initialize parameters
mu = 398600; % Earth gravitational parameter

% Initialize initial conditions
r0 = 6500 ; % initial radius, in km
v0 = 7.8309 ; % initial velocity, in km/s

r0vec = [r0; 0] ;
v0vec = [0; v0] ;

Y0 = [r0vec; v0vec];

% Integration time
t0 = 0;
tf = 86400; % 1 day (or 86400 s)

% Integration options
options = odeset('RelTol', 1e-8, 'AbsTol', 1e-8) ;

% call ode45
[T,Y] = ode45(@twobodyEOM2D, [t0 tf], Y0, options, mu);

% Plot radius over time
for k=1:length(T)
rvec = Y(k,1:2)' ;
radius(k) = norm(rvec) ;
end
figure(1)
plot(T/86400,radius)
xlabel('Time (in days)')
ylabel('orbit radius (in km)')

PROBLEM2 Below is the first order system of differential equations for two-body motion: Assume the following initial conditions and parameters: 0 where u 398600 km/s', R- 10000 km, V -5.8 km/s The goal of this problem is to get familiar with Matlab's ode45 to numerically simulate this two-body orbit.

Explanation / Answer

What do you want to ask. I'm not getting it.

Plz write your question, as you have made a matlab program already.

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