CHAPTER 2 KINEMATICS OF A PARTICLE
Kinematics: It is the study of the geometry of motion of particles, rigid bodies, etc., disregarding the forces associated with these motions. Kinematics of a particle motion of a point in space
1
Interest is on definin
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 7
Due: August 2, 2010
Q1. (see Problem 6-24 in the text). A disk of radius R rotates about its fixed vertical
axis of symmetry at a constant rate . A simple pendulum of length l and particle mass
m is attach
ME 562 ADVANCED DYNAMICS
PURDUE UNIVERSITY
Summer 2010
Instructor:
A. K. Bajaj
Room 368, Mechanical Engineering Building
(Alternatively, Room ME 110)
585 Engineering Mall
Purdue University
West Lafayette, IN 47907-2088
(765) 494-6896 (Office)
(765) 494-57
ME 562 Advanced Dynamics
Summer 2010
Take-Home Midterm Examination
Due July 12, 2010
Honor Code: This is an open-book and open-notes examination. The students can make use of the
textbook and class notes. They can also use the provided solutions of home w
1/11/2010
CHAPTER 1 Introductory Concepts Elements of Vector Analysis Newtons Laws Units The basis of Newtonian Mechanics DAlemberts Principle
1
Science of Mechanics: It is concerned with the motion of material bodies. Bodies have different scales: Micros
Name
PUID
ME562 Spring 2013
7 Purdue University
West Lafayette, iN
Homework Set No. 3
Assignment date: Thursday, January 24
Due date: Thursday, January 31, 5pm
Please include this cover sheet as the rst page of your homework
submission.
Please s
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 6
Due: July 23, 2010
Q1. Two wheels, each of mass m, are connected by a massless axle of length l. Each
wheel is considered to have its mass concentrated as a particle at its hub. The wheels roll
without sli
CHAPTER 6
LAGRANGES EQUATIONS
(Analytical Mechanics)
1
Ex. 1: Consider a particle moving on a
fixed horizontal surface.
z
Let, r P be the
position and F be
the total force on
the particle.
The FBD is:
-mgk
f
O
x
P
F1
y
m (x,y,0)
F1
N
The equation of motio
Reviewing, what we have discussed so far:
Generalized coordinates
Any number of variables (say, n) sufficient
to specify the configuration of the system at
each instant to time (need not be the
minimum number).
In general, let q1 , q2 , qn be generalize
7.13 Eulerian Angles
Rotational degrees of freedom for a rigid
body - three rotations.
If one were to use Lagranges equations to
derive the equations for rotational motion
- one needs three generalized coordinates.
Nine direction cosines with six const
CHAPTER 7
Basic Concepts and Kinematics of Rigid Body
Motion
7.1 Degrees-of-freedom:
F2
F1
(of a rigid body)
m2
m1 f12
f21
Consider three
Z
f23
r1
unconstrained particles
C
O
rC
f32
m
3
r3
m3
F3
X
Y
1
The positions are defined by
r i x i i yi j zi k i = 1
CHAPTER 3
DYNAMICS OF A PARTICLE
Newtons Second Law: It is an experimentally
derived law, valid in a reference frame
Z
Inertial reference frame.
en
XYZ - inertial
path
reference frame
F
P
eb
Let m be mass,
O
et
rOP
rOP- position vector.
X
Then
Y
F F ( r
CHAPTER 4
DYNAMICS OF A SYSTEM OF PARTICLES
We consider a system consisting of n particles
One can treat individual particles, as before;
i.e.,one can draw FBD for each particle,
define a coordinate system and obtain an
expression of the absolute accele
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 1
Assignment Due: 06/09/2010
Q1. Problem 1-1: Forces P and Q are applied to a particle of mass m. The magnitudes of these
forces, P and Q, are constant but the angle between their lines of action can be vari
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 2
Due: June 14, 2010
Q1. Follow the developments in class notes and derive the Frenets
formulas (summarized on page 19 of the Chapter 2 powerpoints) for a
spatial curve. Recall that these formulas relate the
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 3
Due: June 21, 2010
Q1. Consider the particle of mass m located in
the center of a box of sides 2l and constrained to
move in the horizontal plane by the four
identical and linearly elastic springs with spr
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 4
Due: June 28, 2010
Q1. A massless disc of radius R has an embedded particle of mass m at a distance R/2 from the
center. The disc is released from rest in the position shown and rolls without slipping down
ME 562 Advanced Dynamics
Summer 2010
HOMEWORK # 5
Due: July 16, 2010
Q1. (see Problem 6-1 in the text for the figure). A fixed smooth rod makes an angle of 30 with the
floor. A small (negligible radius) ring (say P 1) of mass m can slide on the rod and su