Week 5 Problem Solving: Solutions
Question 1: Drawn from Section 5 material: DAlembert
T
e
e
k
r
L
mg
2
mg
1
1)
Identify the number of degrees of freedom, and the generalised variables.
2 Degrees of Freedom : r,
2)
Express the forces acting on each of the
Week 8 Problem Solving
Question 1: Taken from Section 6 material: Lagrange with friction
q1
k
B
q2
C
R
Fixed
R2
k
1A
Fixed
gravity
m
The above diagram shows a mass attached to a frictionless pulley (A). This pulley
is supported by an unstretchable length
Week 6 Problem Solving
Question 1: Drawn from Section 6 material: Lagrange
Find the equation of motion for the following system using Lagranges equation in terms of
the generalised variable . The runners (A and B) move through the frictionless guides. The
Week 6 Problem Solving: Worked Solutions
Question 1: Drawn from Section 6 material: Lagrange
Find the equation of motion for the following system using Lagranges equation in terms of
the generalised variable . The runners (A and B) move through the fricti
Problem Solving Class: Week 3
Based on material from Section 3: Finite Motion transformations
1. A solar panel is deployed on a satellite by transformation from start location A, to end
location B. This consists of 90 degree rotation about line CD, follow
Week 8 Problem Solving
Question 1: Taken from Section 6 material: Lagrange with friction
Find the Lagrange function and Rayleigh Potential for this system:
k
Fixed
q1
B
C
R
q2
R2
1A
k
Fixed
gravity
m
+
2
Question 2: Taken from Section 7 material: Lagrange
Week 9 Problem Solving
Question 1: Taken from Section 7 material: Lagrange - Electrical
Question 2: Taken from Section 8 material: 1st order equations
Find the first order equations of motions for the following system using:
L
q i
L R
p i
0
qi q i
pi
1
Week 4 Problem Solving: Solutions
Question 1: Drawn from Section 4 material
A)
Use forward kinematics to find the location of point C in reference frame 0 (i.e. x0, y0,
z0) in terms of the geometry of the system and variables: , , s , by using the followi
Problem Solving Class: Week 3
Based on material from Section 3: Finite Motion transformations
1. A solar panel is deployed on a satellite by transformation from start location A, to end
location B. This consists of 90 degree rotation about line CD, follow
Week 2 Problem Solving : Solutions
Question 1: Drawn from Section 2 material
a) Based on the geometry of the cone, find a relationship for the change in height z
as a function in the change in angle .
For one complete revolution 2 the change in z is d
The