Changing Length of Pendulum while it is in motion

Hi

I have seen many simulations of pendulums oscillating found on matlab. One such example can be found in this link. The link provides the code to simulate and visualise the oscillation of the pendulum by setting up different initial fixed parameters. I was wondering if it is possible to simulate the length of the rod, attached to the pendulum, changing while the pendulum is in motion( i.e the length of the rod should be able to increase/decrease such that it reaches the target length specified over a fixed period of time). This would also mean that the rate of change of the length of the rod can also be controlled.

Currently, using a ode45 solver, I am able to plot the path of the pendulum's oscillation. This is done through specifying the initial conditions, which are fixed. Hence, is there a way that the length of the rod attached to the pendulum be modified during the oscillation?

Thank you in advance!!!

[KSSV]

Are you talking about spring pendulum?

https://in.mathworks.com/matlabcentral/fileexchange/33168-springpendulum

[Humberto Ramos]

Check this out:

https://www.mathworks.com/matlabcentral/fileexchange/88516-variable-length-pendulum

Answer 1

[Mischa Kim]

Dear Yan Koon Ang,

this is possible. In the example you are referring to in your question you would have to make the time variable t available in the ode file and then you could do something like this:

function xdot = Equation(t,x)
% Set the input values in order to pass onto ode45
% [...]
L = x(5) * (1 + 0.5*t); % replace by whatever behavior/equation you need

[Yan Koon Ang]

Hi Mischa Kim,

I am new to this, hence could you please elaborate on how I could modify the code to allow the time variable " t " available in the ode file (Animation.m file).

Thank you for your understanding!

function Animation(ivp, duration, fps, movie, arrow)
% [...]
nframes=duration*fps; % Number of Frames
% Solving the Equation using ode45
sol=ode45(@Equation,[0 duration], ivp); 
t = linspace(0,duration,nframes);
y = deval(sol,t);

[Mischa Kim]

The first changes you need to make are in the Equation() function, as pointed out above. Just browsing through the example files in the link you provided you need to adapt the Anmiation() function accordingly:

% Position and Angular velocity
phi = y(1,:)';
dtphi = y(2,:)';
L = ivp(5)*(1 + 0.5*t); % replace by whatever behavior/equation you need
% To set the Range os Phase plane, time vs. depl plots

L is used further below to scale the axis. range is a scalar, L a vector, so, e.g.

range = 1.1*L(1);

There may be more changes to get you exactly what you need, but this should get you started.

Answer 2

[Humberto Ramos]

Check this out:

https://www.mathworks.com/matlabcentral/fileexchange/88516-variable-length-pendulum