[GSoC] JointsMethod

[sidhu1012]

@moorepants For JointsMethod, I think it would be wise for me to complete Sahil's PR #9835.

My idea for JointsMethod is something like:-

J = JointsMethod(Newtonion frame/body, *joints)

An example would be Multi degree of freedom holonomic system

>>> W = Body('W') # Wall
>>> B = Body('B') # Block
>>> P = Body('P') #Pendulum
>>> b = Body('b') # bob

# Defining coordinates and speeds
>>> q1, q2, q3 = dynamicsymbols('q1, q2, q3') # coordinates
>>> u1, u2, u3 = dynamicsymbols('u1 u2 u3') # speeds

# Form joints to do kinematics
>>> J1 = PrismaticJoint('J1', W, B, q1, u1)
>>> J2 = PinJoint('J2', B, P, q2, u2)
>>> J3 = PinJoint('J3', P, b, q3, u3)

# Specified forces
>>> F, T = dynamicsymbols('F T')
>>> k, c, g, kt = symbols('k c g kt')

# Applying forces now
>>> B.apply_force(F)
>>> apply_force(k*q1, W, B) #Spring force
>>> apply_force(c*q1.diff(), W, B) #dampner
>>> P.apply_force(P.mass*g)
>>> b.apply_force(b.mass*g)

# Applying torques now
>>> apply_torque(kT*q3, P, b)
>>> P.apply_torque(T)

# Solving using KDEs using JointsMethod(Kane)
>>> S = JointsMethod(W, J1, J2, J3) # Wall is Newtonian frame
 # We can add all Kane's Method required attributes to Joints Method to make it a bit analogous

[moorepants]

Here is my suggested adjustments (also I think this may be complete for that actual problem).

from sympy import zeros, symbols
from sympy.physics.mechanics import (dynamicsymbols, Body, PrismaticJoint,
                                     PinJoint, apply_constant_gravity,
                                     JointsMethod)

l, k, c, g, kT = symbols('l, k, c, g, kT')
ma, mb, mc, IBzz = symbols('ma, mb, mc, IBzz')
q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1, q2, q3, u1, u2, u3')
F, T = dynamicsymbols('F, T')

# bodies
wall = Body('N')
block = Body('A', mass=ma)
IB = zeros(3, 3)
IB[2, 2] = IBzz
compound_pend = Body('B', mass=mb, central_inertia=IB)
simple_pend = Body('C', mass=mc, central_inertia=0)
bodies = (wall, block, compound_pend, simple_pend)

# joints
slider = PrismaticJoint('J1', wall, block, coordinate=q1, speed=u1)
rev1 = PinJoint('J2', block, compound_pend, coordinate=q2, speed=u2,
                child_axis=compound_pend.z, child_pos=l*2/3*compound_pend.y,
                parent_axis=compound_pend.z)
rev2 = PinJoint('J3', compound_pend, simple_pend, coordinate=q3, speed=u3,
                child_axis=compound_pend.z, child_pos=-l/3*compound_pend.y,
                parent_axis=simple_pend.z, parent_pos=l*simple_pend.y)
joints = (slider, rev1, rev2)

# loads
block.apply_force(F*block.x)
block.apply_force(-k*q1*block.x, body=wall)
block.apply_force(-c*u1*block.x, body=wall)
compound_pend.apply_torque(T*compound_pend.z, body=block)
simple_pend.apply_torque(kT*q3*simple_pend.z, body=compound_pend)
apply_constant_gravity(-wall.y, g, *bodies)

# equations of motion
method = JointsMethod(wall, *joints)
eqs = method.calculate_equations_of_motion()

[sidhu1012]

We dont have any apply_constant_gravity() , gravity would be applied using .apply_force() only.

[moorepants]

We dont have any apply_constant_gravity() , gravity would be applied using .apply_force() only.

Yes, I'm aware.

[sidhu1012]

@moorepants Do we need another function like we do in Kane's method because I think you didn't recommend using a function after declaring the Kane's method.

method = JointsMethod(wall, *joints)

After it we could directly do
method.fr and method.frstar

rather than doing
method.calculate_equations_of_motions()

I prefer the 2nd one.

[moorepants]

# We can add all Kane's Method required attributes to Joints Method to make it a bit analogous

It would be key to make sure this Method class works with PyDy's system:

https://pydy.readthedocs.io/en/latest/system.html

[sidhu1012]

Yes, I have already added all attributes of Kane's method

[moorepants]

Thinking about applying a constant gravity force to all bodies more. Maybe we should have a function that applies the same force to a collection of bodies's mass center. Some ideas:

apply_same_force(F*A.x, body1, body2, body3, ...)  # applies the force F*A.x to each body's mass center
apply_same_torque(T*A.z, body1, body2, body3, ...)  # applies the same torque T*A.z to each bodies' frame
apply_same_force(F*A.x, (body1, point1), (body2, point2), (body3, point3))  # applies same force to each point and attaches the force to the body 

Not sure we need the last one, but there could be use cases.

So maybe any function we create is just to support applying to multiple bodies at once.

But this works too:

for body in bodies:
    body.apply_force(F*A.x)

Which is simple, so maybe we don't need a function for this very simple loop.

[sidhu1012]

I think we can use loops for this simple case and doesn't require any special function for that.