Add acceleration to a simple pendulum

[Raphael Timbó]

Hi,

I saw the example for the simple pendulum on pydy's github repository (https://github.com/pydy/pydy/blob/master/examples/simple_pendulum/run.py).

I wanted to go from the simple pendulum shown in figure below case (a) to the pendulum with the acceleration on u2, case(b).

Looking at the code, I thought that the solution was adding acceleration to point 'O':

 (O.set_acc(N, att * N.y)

But this does not seem to work.

Can someone point me in the right direction?

Thank you!

Att,

Raphael

[Jason Moore]

Raphael,

Can you share your code and the resulting equations of motion?

Jason
moorepants.info
+01 530-601-9791

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[Raphael Timbó]

Hi Jason!

So, I took the code from the example and added the symbol a and the following two lines of code:

# This code requires sympy 1.0 to run
	from sympy import *
	from sympy.physics.mechanics import LagrangesMethod, Lagrangian
	from sympy.physics.mechanics import ReferenceFrame, Particle, Point
	from sympy.physics.mechanics import dynamicsymbols
	# System state variables
	theta = dynamicsymbols('theta')
	thetad = dynamicsymbols('theta', 1)
	# Other system variables
	m, l, g, a = symbols('m l g a')
	# Set up the reference frames
	# Reference frame A set up in the plane perpendicular to the page containing
	# segment OP
	N = ReferenceFrame('N')
	A = N.orientnew('A', 'Axis', [theta, N.z])
	# Set up the points and particles
	O = Point('O')
	P = O.locatenew('P', l * A.x)
	Pa = Particle('Pa', P, m)
	# Set up velocities
	A.set_ang_vel(N, thetad * N.z)
	O.set_vel(N, 0) O.set_acc(N, a * N.y) # ----------------------------------------------------------------> Added line
	P.v2pt_theory(O, N, A) P.a2pt_theory(O, N, A) # ----------------------------------------------------------------> Added line
	# Set up the lagrangian
	L = Lagrangian(N, Pa)
	# Create the list of forces acting on the system
	fl = [(P, g * m * N.x)]
	# Create the equations of motion using lagranges method
	l = LagrangesMethod(L, [theta], forcelist=fl, frame=N)
	pprint(l.form_lagranges_equations())

As a result I am getting:

Matrix([[g*l*m*sin(theta(t)) + l**2*m*Derivative(theta(t), t, t)]])

Which is the simple pendulum's equation of motion, so nothing has changed (was expecting an extra term - m*a* l*cos𝜃)

I thought that maybe I had to change something with the reference frame, but I could not find a solution.

Thanks for the help!

Att, 
Raphael

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Att,

Raphael Timbó

Mechanical Engineer at Petrobras

email: raph...@gmail.com

[Jason Moore]

Lagrange's method uses the velocities of particles and rigidbodies to compute the equations of motion. As it stands you have the velocity of the base set to 0 and the acceleration you set is never used internally in LagrangesMethod.

Jason
moorepants.info
+01 530-601-9791

[Raphael Timbó]

I got it. Thought I could go to the acceleration directly...

Since the acceleration in the problem that I have is (a/2)*t**2, I have set the velocity as 'a*t' and now I am getting the expected result. 

Thank you very much!!!

[Raphael Timbó]

I got it. Thought I could go to the acceleration directly...

Since the displacement in the problem that I have is (a/2)*t**2, I have set the velocity as 'a*t' and now I am getting the expected result. 

Thank you very much!!!

On Wed, Aug 31, 2016 at 6:22 PM, Jason Moore <moore...@gmail.com> wrote: