Solve ordinary differential equations with events
% To simulate a ball bouncing off stair case after dropping from a height of
% 10meters onto a stair case starting from 5meters. Let the stair case be
% defined by the function y(x) = 5-floor(x). And the ball rolled off an edge
% at height of 10meters with velocity of 0.5m/s.
% The system of first order differential equation is:
odefun = @(t,y) [0.5; y(3); -9.8];
% Initial condition is:
initcon = [0, 10, 0];
% Time span of the simulation:
tspan = [0,20];
% Since we want the ball to bounce off the stair case, the effect condition is:
effectcon = @(t,y) [y(2) - (5-floor(y(1))),1,-1];
% The effect matrix is to recoil only the vertical velocity with restitution of 0.8:
effectmat = [1,0,0;0,1,0;0,0,-0.8];
% Solve the differential equation:
[t,y] = SolveOdeWithEvent(odefun, initcon, tspan, effectcon, effectmat);
% Generate the absisca for the stair case
x = linspace(y(1,1),y(end,1),10000);
% Animate the result.
figure
r = 0:0.01*pi:2*pi;
cx = 0.1*cos(r); cy = 0.1*sin(r);
plot(x,5-floor(x)); ; axis equal; hold on
c = plot(cx + y(1,1),cy + y(1,2) + 0.1);
axis([min(y(:,1)),max(y(:,1)),min(y(:,2)),max(y(:,2))]);
drawnow
for tt = 0.03:0.03:t(end)
xy = interp1(t,y,tt);
c.XData = cx + xy(1);
c.YData = cy + xy(2) + 0.1;
drawnow;
end
Zitieren als
Lateef Adewale Kareem (2024). Solve ordinary differential equations with events (https://www.mathworks.com/matlabcentral/fileexchange/71586-solve-ordinary-differential-equations-with-events), MATLAB Central File Exchange. Abgerufen .
Kompatibilität der MATLAB-Version
Plattform-Kompatibilität
Windows macOS LinuxKategorien
- MATLAB > Mathematics > Numerical Integration and Differential Equations > Ordinary Differential Equations >
Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Live Editor erkunden
Erstellen Sie Skripte mit Code, Ausgabe und formatiertem Text in einem einzigen ausführbaren Dokument.
SolveOdeWithEvent
Version | Veröffentlicht | Versionshinweise | |
---|---|---|---|
1.0.0 |