Advanced Dynamics
Rami Alkhatib
Lecture 03
1
Learning Outcomes
Define Kinetics
State Newtons Laws for Particles
Derive Eulers First Law for motion of the mass center of bodies
Calculate the location of the mass center for a composite body
2
3
Newtons
Advanced Dynamics
Rami Alkhatib
Lecture 04
1
2
Learning Outcomes
Define Rigid Body Kinematics
Identify three types of Planar Rigid Body Motion
Derive the Relative Velocity Equation
3
4
5
6
Example
The crank arm B1 turns about fixed point O with an angu
Advanced Dynamics
Rami Alkhatib
Lecture 05
1
Learning Outcome
Determine the acceleration of the center of the wheel and the
acceleration of the point of contact for a wheel:
Rolling on a fixed straight surface
Rolling on a fixed plane curve
2
3
4
5
Lea
Advanced Dynamics
Rami Alkhatib
Lecture 01
Newtons Laws and Eulers Laws;
Work-Energy Principle
Rigid Body Kinematics I
Angular Velocity; Angular Acceleration
Velocities in Moving Reference Frames; Accelerations in Moving Reference Frames; The Earth as a
M
Kinematics for 2.003, Fall 2010
1
Some Basics on Frames and Derivatives of Vectors
Kinematics is all about reference frames, vectors, dierentiation, constraints and coordinates.
1. A reference frame is a perspective from which a system is observed. We rep
2.004 MODELING DYNAMICS AND CONTROL II
Spring 2003
Problem Set No. 2
Problem 1
A fender is mounted to a vehicle via two shock absorbers as depicted in the sketch.
Shock absorber
Fender
Vehicle
Barrier
Figure 1
Each shock absorber can be approximately desc
2.003SC
Recitation 3 Notes: V and A of a Point in a Moving Frame
Velocity and Acceleration of a Point in a Moving Frame
The gure below shows a point B in a coordinate system Axyz which is translating and rotating with
respect to a xed coordinate system
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Recitation 2 Notes: Planar Motion
Amusement Park Ride - Problem Statement
A ride at an amusement park consists of four symmetrically located seats, driven to rotate about the
vertical axis A at a constant rate of 2 rev/min, with respect to the sup
KTH Mechanics
2010 10 21
Rigid Body Dynamics, SG2150
Exam, 2010 10 21, kl 09.00-13.00
Calculational problems
Problem 1: A slender rod AB of mass m and length 2a, rests on a smooth horizontal
plane. A small ball of the same mass m impacts with the rod at i
KTH Mechanics
2010 10 21
Rigid Body Dynamics, SG2150
Solutions to Exam, 2010 10 21
Calculational problems
Problem 1: A slender rod AB of mass m and length 2a, rests on a smooth horizontal
plane. A small ball of the same mass m impacts with the rod at its
KTH Mechanics
2013 10 25
Rigid Body Dynamics, SG2150
Solutions to Exam, 2013 10 25
Calculational problems
Problem 1: A block of mass M can slide freely along a straight horizontal track. A rod
of mass m and length a is hinged with one end at the center of
KTH Mechanics
2013 10 25
Rigid Body Dynamics, SG2150
Exam, 2013 10 25, kl 14.00-18.00
Calculational problems
Problem 1: A block of mass M can slide freely along a straight horizontal track. A rod
of mass m and length a is hinged with one end at the center
2.003SC
Recitation 8 Notes: Cart and Pendulum (Lagrange)
Cart and Pendulum - Problem Statement
A cart and pendulum, shown below, consists of a cart of mass, m1 , moving on a horizontal surface, acted
upon by a spring with spring constant k. From the cart