Numerically integrating Acceleration to get displacement?
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I want to rephrase my last question, as i was not very clear there.
What i am trying to do is integrate the following second order, nonlinear ode, which is an expression for angular acceleration,
twice, to get the displacement, and compare it with the actual expression for displacement:
BOTH ω and A are specified initially. They are constants.
------------------------------------equation for acceleration
(corrected from )
if initial conditions are required, then x(0)=pi/4 and dx/dt (t=0) =0
this has to be integrated w.r.t time, t, twice, between the limits t=0 and t=50 (it can be any time interval)
im not sure if the interval for x has to be defined as well.
the equation for displacement is
-----------------------------------------equation for displacement (corrected from
Any help would be appreciated!
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Ameer Hamza
2020년 11월 15일
Are you sure that the equations are correct? The solution you posted does not satisfy the initial conditions.
Generally, such a problem can be solved using the Symbolic toolbox
syms x(t) w A
dxdt = diff(x);
dx2dt2 = diff(x,2);
ode = dx2dt2 == -A*w*sin(dxdt);
cond = [x(0)==pi/4 dxdt(0)==0];
sol = dsolve(ode, cond)
or ode45() can be used for a numerical solution.
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Ameer Hamza
2020년 11월 15일
Yes, in that case, initial conditions will be zero and you can use cumtrapz().
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