jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved) Edit View Insert Cell Kernel Widgets Help File + in 101: Run ↑ C Markdown #Position vectors or mass centers or roas relative to the mass center S r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0]) r_G2_Sstar= sp.Matrix ([0, -b/2, 0]) r_G3_Sstar=sp.Matrix ([0, 0, -b/2]) P #Inertia matrices of rods about S* using the parallel axis theorem I_R1_Sstar=I_G1 + m * (r_Gl_Sstar.dot (r_Gl_Sstar) *sp.eye (3) - r_G1_Sstar*r_G1_Sstar.T) I_R2_Sstar=I_G2 + m * (r_G2_Sstar.dot (r_G2_Sstar) *sp.eye (3) - r_G2_Sstar*r_G2_Sstar.T) I_R3_Sstar = I_G3 + m* (r_G3_Sstar.dot (r_G3_Sstar)*sp.eye (3) - r_G3_Sstar*r_G3_Sstar.T) In [9]: # Moment of inertia matrix of the system about S* I_matrix_S_about_Sstar = I_R1_Sstar + I_R2_Sstar + I_R3_Sstar #Angular velocity vector of the system angular_velocity sp.Matrix ([omega, omega, omega]) In [10]: # Angular momentum of rods about point o H_R1_0= I_G1 angular_velocity + mr_Gl_Sstar.cross (r_G1_Sstar.cross (angular_velocity)) BRZ_O = I_G2 * angular_velocity + m * r_G2_Sstar.cross (r_G2_Sstar.cross (angular_velocity)) H_R3_0= I_G3* angular_velocity + mr_G3_Sstar.cross (r_G3_Sstar.cross (angular_velocity)) #Angular momentum of the system about point o H_S_about_0= H_R1_0+ H_R2_0+ H_R3_0 In [11]: # Magnitude of the angular momentum of the system about point o H_S_about_0_magnitude = H_S_about_0.norm() Trusted print("Moment of inertia matrix of the system about S*:") print (I_matrix_S_about_Sstar) print("\nMagnitude of the angular momentum of the system about point 0:") print (H_S_about_0_magnitude) File "/var/folders/nk/sfvkdtp13jz_9vg5qxdyqjf00000gn/T/ipykernel_1537/4081370202.py", line 7 print("\nMagnitude of the angular momentum of the systèm about point 0:") print (H_S_about_0_magnitude) SyntaxError: invalid syntax Logout Python 3 (ipykernel) O Jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved) Kernel Widgets File + Edit View Insert Cell Help ▶ Run C>>> Markdown In [ ]: from sympy import symbols, sin, cos, Matrix www from sympy.physics.mechanics import ReferenceFrame, Point, dynamicsymbols omega dynamicsymbols (omega') m, 1, b = symbols ('m 1 b') Enter Your Solution Below Add as many cells as needed to compute your answers to both questions above. In [1]: import sympy as sp # Define symbols m, 1, b, omega= sp.symbols ('m 1 b omega') Ix= 1/12 * m* 1**2 In [2] # Inertia matrices of rods about their mass centers (G) I_G1= sp.Matrix ([[0, 0, 0], [0, Ix, 0], [0, 0, Ix]]) I_G2 = sp.Matrix ([[Ix, 0, 0], [0, 0, 0], [0, 0, Ix]]) I_G3 = sp.Matrix ([[Ix, 0, 0], [0, Ix, 0], [0, 0, 011) In [8]: # Position vectors of mass centers of rods relative to the mass center S* r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0]) r_G2_Sstar = sp.Matrix ( [0, -b/2, 0]) r_G3_Sstar = sp.Matrix( [0, 0, -b/2]) # Inertia matrices of rods about S* using the parallel axis theorem I_R1_Sstar = I_G1 + m (r_G1_Sstar.dot (r_G1_Sstar) *sp.eye (3) r_G1_Sstar*r_G1_Sstar.T) r_G2_Sstar*r_G2_Sstar.T) I_R2_Sstar = I_G2 + m (r_G2_Sstar.dot (r_G2_Sstar) *sp.eye (3) * I_R3_Sstar = I_G3+ m (r_G3_Sstar.dot (r_G3_Sstar) *sp.eye (3) - r_G3_Sstar*r_G3_Sstar.T) * In [9]: # Moment of inertia matrix of the system about S* I_matrix_S_about_Sstar=I_R1_Sstar + I_R2_Sstar+I_R3_Sstar #Angular velocity vector of the system angular_velocity sp.Matrix( [omega, omega, omega]) Trusted Logout Python 3 (ipykernel) O

jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved) Edit View Insert Cell Kernel Widgets Help File + in 101: Run ↑ C Markdown #Position vectors or mass centers or roas relative to the mass center S r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0]) r_G2_Sstar= sp.Matrix ([0, -b/2, 0]) r_G3_Sstar=sp.Matrix ([0, 0, -b/2]) P #Inertia matrices of rods about S* using the parallel axis theorem I_R1_Sstar=I_G1 + m * (r_Gl_Sstar.dot (r_Gl_Sstar) sp.eye (3) - r_G1_Sstarr_G1_Sstar.T) I_R2_Sstar=I_G2 + m * (r_G2_Sstar.dot (r_G2_Sstar) sp.eye (3) - r_G2_Sstarr_G2_Sstar.T) I_R3_Sstar = I_G3 + m* (r_G3_Sstar.dot (r_G3_Sstar)sp.eye (3) - r_G3_Sstarr_G3_Sstar.T) In [9]: # Moment of inertia matrix of the system about S* I_matrix_S_about_Sstar = I_R1_Sstar + I_R2_Sstar + I_R3_Sstar #Angular velocity vector of the system angular_velocity sp.Matrix ([omega, omega, omega]) In [10]: # Angular momentum of rods about point o H_R1_0= I_G1 angular_velocity + mr_Gl_Sstar.cross (r_G1_Sstar.cross (angular_velocity)) BRZ_O = I_G2 * angular_velocity + m * r_G2_Sstar.cross (r_G2_Sstar.cross (angular_velocity)) H_R3_0= I_G3* angular_velocity + mr_G3_Sstar.cross (r_G3_Sstar.cross (angular_velocity)) #Angular momentum of the system about point o H_S_about_0= H_R1_0+ H_R2_0+ H_R3_0 In [11]: # Magnitude of the angular momentum of the system about point o H_S_about_0_magnitude = H_S_about_0.norm() Trusted print("Moment of inertia matrix of the system about S:") print (I_matrix_S_about_Sstar) print("\nMagnitude of the angular momentum of the system about point 0:") print (H_S_about_0_magnitude) File "/var/folders/nk/sfvkdtp13jz_9vg5qxdyqjf00000gn/T/ipykernel_1537/4081370202.py", line 7 print("\nMagnitude of the angular momentum of the systèm about point 0:") print (H_S_about_0_magnitude) SyntaxError: invalid syntax Logout Python 3 (ipykernel) O Jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved) Kernel Widgets File + Edit View Insert Cell Help ▶ Run C>>> Markdown In [ ]: from sympy import symbols, sin, cos, Matrix www from sympy.physics.mechanics import ReferenceFrame, Point, dynamicsymbols omega dynamicsymbols (omega') m, 1, b = symbols ('m 1 b') Enter Your Solution Below Add as many cells as needed to compute your answers to both questions above. In [1]: import sympy as sp # Define symbols m, 1, b, omega= sp.symbols ('m 1 b omega') Ix= 1/12 m* 1**2 In [2] # Inertia matrices of rods about their mass centers (G) I_G1= sp.Matrix ([[0, 0, 0], [0, Ix, 0], [0, 0, Ix]]) I_G2 = sp.Matrix ([[Ix, 0, 0], [0, 0, 0], [0, 0, Ix]]) I_G3 = sp.Matrix ([[Ix, 0, 0], [0, Ix, 0], [0, 0, 011) In [8]: # Position vectors of mass centers of rods relative to the mass center S* r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0]) r_G2_Sstar = sp.Matrix ( [0, -b/2, 0]) r_G3_Sstar = sp.Matrix( [0, 0, -b/2]) # Inertia matrices of rods about S* using the parallel axis theorem I_R1_Sstar = I_G1 + m (r_G1_Sstar.dot (r_G1_Sstar) sp.eye (3) r_G1_Sstarr_G1_Sstar.T) r_G2_Sstarr_G2_Sstar.T) I_R2_Sstar = I_G2 + m (r_G2_Sstar.dot (r_G2_Sstar) sp.eye (3) * I_R3_Sstar = I_G3+ m (r_G3_Sstar.dot (r_G3_Sstar) sp.eye (3) - r_G3_Sstarr_G3_Sstar.T) * In [9]: # Moment of inertia matrix of the system about S* I_matrix_S_about_Sstar=I_R1_Sstar + I_R2_Sstar+I_R3_Sstar #Angular velocity vector of the system angular_velocity sp.Matrix( [omega, omega, omega]) Trusted Logout Python 3 (ipykernel) O

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jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved)
Edit View Insert Cell
Kernel Widgets Help
File
+
in 101:
Run
↑
C
Markdown
#Position vectors or mass centers or roas relative to the mass center S
r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0])
r_G2_Sstar= sp.Matrix ([0, -b/2, 0])
r_G3_Sstar=sp.Matrix ([0, 0, -b/2])
P
#Inertia matrices of rods about S* using the parallel axis theorem
I_R1_Sstar=I_G1 + m * (r_Gl_Sstar.dot (r_Gl_Sstar) *sp.eye (3) - r_G1_Sstar*r_G1_Sstar.T)
I_R2_Sstar=I_G2 + m * (r_G2_Sstar.dot (r_G2_Sstar) *sp.eye (3) - r_G2_Sstar*r_G2_Sstar.T)
I_R3_Sstar = I_G3 + m* (r_G3_Sstar.dot (r_G3_Sstar)*sp.eye (3) - r_G3_Sstar*r_G3_Sstar.T)
In [9]: # Moment of inertia matrix of the system about S*
I_matrix_S_about_Sstar = I_R1_Sstar + I_R2_Sstar + I_R3_Sstar
#Angular velocity vector of the system
angular_velocity sp.Matrix ([omega, omega, omega])
In [10]: # Angular momentum of rods about point o
H_R1_0= I_G1 angular_velocity + mr_Gl_Sstar.cross (r_G1_Sstar.cross (angular_velocity))
BRZ_O =
I_G2 * angular_velocity + m * r_G2_Sstar.cross (r_G2_Sstar.cross (angular_velocity))
H_R3_0= I_G3* angular_velocity + mr_G3_Sstar.cross (r_G3_Sstar.cross (angular_velocity))
#Angular momentum of the system about point o
H_S_about_0= H_R1_0+ H_R2_0+ H_R3_0
In [11]: # Magnitude of the angular momentum of the system about point o
H_S_about_0_magnitude = H_S_about_0.norm()
Trusted
print("Moment of inertia matrix of the system about S*:")
print (I_matrix_S_about_Sstar)
print("\nMagnitude of the angular momentum of the system about point 0:") print (H_S_about_0_magnitude)
File "/var/folders/nk/sfvkdtp13jz_9vg5qxdyqjf00000gn/T/ipykernel_1537/4081370202.py", line 7
print("\nMagnitude of the angular momentum of the systèm about point 0:") print (H_S_about_0_magnitude)
SyntaxError: invalid syntax
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Python 3 (ipykernel) O

Jupyter Problem 1 Last Checkpoint: 7 hours ago (autosaved)
Kernel Widgets
File
+
Edit View
Insert
Cell
Help
▶ Run C>>> Markdown
In [ ]: from sympy import symbols, sin, cos, Matrix
www
from sympy.physics.mechanics import ReferenceFrame, Point, dynamicsymbols
omega dynamicsymbols (omega')
m, 1, b = symbols ('m 1 b')
Enter Your Solution Below
Add as many cells as needed to compute your answers to both questions above.
In [1]: import sympy as sp
# Define symbols
m, 1, b, omega= sp.symbols ('m 1 b omega')
Ix= 1/12 * m* 1**2
In [2] # Inertia matrices of rods about their mass centers (G)
I_G1= sp.Matrix ([[0, 0, 0], [0, Ix, 0], [0, 0, Ix]])
I_G2 = sp.Matrix ([[Ix, 0, 0], [0, 0, 0], [0, 0, Ix]])
I_G3 = sp.Matrix ([[Ix, 0, 0], [0, Ix, 0], [0, 0, 011)
In [8]: # Position vectors of mass centers of rods relative to the mass center S*
r_Gl_Sstar = sp.Matrix ([-b/2, 0, 0])
r_G2_Sstar = sp.Matrix ( [0, -b/2, 0])
r_G3_Sstar = sp.Matrix( [0, 0, -b/2])
# Inertia matrices of rods about S* using the parallel axis theorem
I_R1_Sstar = I_G1 + m
(r_G1_Sstar.dot (r_G1_Sstar) *sp.eye (3)
r_G1_Sstar*r_G1_Sstar.T)
r_G2_Sstar*r_G2_Sstar.T)
I_R2_Sstar = I_G2 + m (r_G2_Sstar.dot (r_G2_Sstar) *sp.eye (3)
*
I_R3_Sstar = I_G3+ m (r_G3_Sstar.dot (r_G3_Sstar) *sp.eye (3) - r_G3_Sstar*r_G3_Sstar.T)
*
In [9]: # Moment of inertia matrix of the system about S*
I_matrix_S_about_Sstar=I_R1_Sstar + I_R2_Sstar+I_R3_Sstar
#Angular velocity vector of the system
angular_velocity sp.Matrix( [omega, omega, omega])
Trusted
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