THE FUNCTION odefun IS NESTED SO THE ENTIRE CODE BELOW SHOULD BE SAVED AS ONE FILE coriolis.m:
%
function coriolis
clc,clear,close all
%% coriolis.m
% let dxdt = p, dydt = q
%% part a)
%
R = 1;
v0 = 1.1854; theta = -1.0039; Tfinal = pi;
x0 = R; y0 = 0; p0 = -v0*cos(theta); q0 = v0*sin(theta);
cond = [x0 y0 p0 q0];
% solving with ode45
t = linspace(0,Tfinal,100);
[T,SOL] = ode45(@odefun,t,cond);
X = SOL(:,1)
Y = SOL(:,2)
% plotting the solution
figure
plot(X,Y,'- b')
xlabel('x(t)'),ylabel('y(t)')
title(['(v0,theta,Tfinal) = (' num2str(v0) ',' num2str(theta) ','
num2str(Tfinal) ')']),grid on
%% part b)
%
R = 1;
v0 = 1.0223; theta = -1.3617; Tfinal = 3*pi;
x0 = R; y0 = 0; p0 = -v0*cos(theta); q0 = v0*sin(theta);
cond = [x0 y0 p0 q0];
% solving with ode45
t = linspace(0,Tfinal,100);
[T,SOL] = ode45(@odefun,t,cond);
X = SOL(:,1);
Y = SOL(:,2);
% plotting the solution
figure
plot(X,Y,'- b')
xlabel('x(t)'),ylabel('y(t)')
title(['(v0,theta,Tfinal) = (' num2str(v0) ',' num2str(theta) ','
num2str(Tfinal) ')']),grid on
%% part c)
%
R = 1;
v0 = 1.0081; theta = -1.4442; Tfinal = 5*pi;
x0 = R; y0 = 0; p0 = -v0*cos(theta); q0 = v0*sin(theta);
cond = [x0 y0 p0 q0];
% solving with ode45
t = linspace(0,Tfinal,100);
[T,SOL] = ode45(@odefun,t,cond);
X = SOL(:,1);
Y = SOL(:,2);
% plotting the solution
figure
plot(X,Y,'- b')
xlabel('x(t)'),ylabel('y(t)')
title(['(v0,theta,Tfinal) = (' num2str(v0) ',' num2str(theta) ','
num2str(Tfinal) ')']),grid on
%% function to express the ode as a system of equations
%
function [ ode ] = odefun(t,in)
% dxdt = p, dydt = q
%
omega = 1;
%
x = in(1); y = in(2); p = in(3); q = in(4);
%
dxtd = p; % x'
dydt = q; % y'
dpdt = 2*omega*q + omega^2*x; % x''
dqdt = -2*omega*p + omega^2*y; % y''
%
ode = [
dxtd;
dydt;
dpdt;
dqdt;
];
end
end
------------------------------------------------------------------------------
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