How to solve spring-mass ODE in rotating frame (without symbolic toolbox)

Hi,

I am trying to solve the ODE of a spring & mass in the rotating frame.

The equations of motion are as follows:

mx'' = -kx + 2my'w + m(x + e)w^2
my'' = -ky - 2mx'w + myw^2

here the "eccentric mass" is aligned with the x axis.

Given a set of initial conditions - what tool can i use in MATLAB to solve for x(t), y(t)?

Any help would be greatly appreciated!!!

Thanks!

Answer 1

[Steven Lord]

Start off trying the ode45 function. Use the "Solve Nonstiff Equation" and "ODE with Time-Dependent Terms" examples on that documentation page as a model for writing your own ODE function and pass a function handle to that ODE function into ode45 as the first input argument.

If ode45 doesn't work or takes too long, try a stiffer solver from the table in the Basic Solver Selection section on this documentation page.

[Tyler]

Thank you for the direction!

I have pout together the following:

function [t,y] = SDRF(k, m, w, e,  initialRad, initialRadVel, initialAngle, ti, tf)     % ‘SDRF’ for ‘Spring-Mass Rotating Frame’

% Physical Parameters

% k = 1;     % stiffness, lbf/in
% m = 5;     % mass, lbm
% w = 0.007; % rotational speed, rad/s
% e = 2;     % mass eccentricity

% Initial Conditions

%initialRad = 1.3;
%initialRadVel = 0;
%initialAngle = pi/4;
initialAngleVel = w;

%ti = 0;
%tf = 120;

%     initial X, initial X', initial Y, initial Y'
ic = [initialRad; initialRadVel; initialAngle; initialAngleVel];
tspan = [ti tf];

% Equations of motion
% y(1) = X1
% y(2) = X2 = X1'
% y(3) = Y1
% y(4) = Y2 = Y1'

[t,y] = ode45(@odefun, tspan, ic);

      function dydt = odefun(t,y)
          dydt = zeros(4,1);
          dydt(1) = y(2);
          dydt(2) = -(k/m)*y(1)+2*y(4)+(y(1)+e)*w^2;
          dydt(3) = y(4);
          dydt(4) = -(k/m)*y(3)+2*y(2)+y(3)*w^2;
      end

%plot(t,y,'-o')

end

I am not quite getting what i want out of the output - but can you confirm that the function was set up properly as intended per original post? if that is set up properly i can fiddle with the rest!

Thanks so much!

[James Tursa]

It looks like you are missing a w in your odefun for the 2my'w and 2mx'w terms. Also the sign of one of the terms looks incorrect. Try this:

          dydt(2) = -(k/m)*y(1) + 2*y(4)*w + (y(1)+e)*w^2;
            :
          dydt(4) = -(k/m)*y(3) - 2*y(2)*w + y(3)*w^2;

[Tyler]

Thank you! You are right, i was missing the w, and the sign was wrong on the 2nd term of the 4th dydt eqn.