Lecture #10 Part #1 POWER AND EFFICIENCY
Today s Objectives:
Students will be able to:
1. Determine the power generated
by a machine, engine, or motor.
2. Calculate the mechanical
efficiency of a machine.
In-Class Activities:
Reading Quiz
Applications
Lecture #5 Part #1 ABSOLUTE DEPENDENT MOTION
ANALYSIS OF TWO PARTICLES
Today s Objectives:
Students will be able to:
1. Relate the positions, velocities,
and accelerations of particles
undergoing dependent motion.
In-Class Activities:
Reading Quiz
Appli
Lecture #22 PLANAR KINETICS OF A RIGID
BODY: CONSERVATION OF ENERGY
Today s Objectives:
Students will be able to:
a) Determine the potential
energy of conservative forces.
b) Apply the principle of
conservation of energy.
In-Class Activities:
Reading Qui
Lecture #20 Part #1 EQUATIONS OF MOTION:
ROTATION ABOUT A FIXED AXIS
Today s Objectives:
Students will be able to:
1. Analyze the planar kinetics
of a rigid body undergoing
rotational motion.
In-Class Activities:
Reading Quiz
Applications
Rotation Abou
Lecture #20 Part #1 EQUATIONS OF MOTION:
ROTATION ABOUT A FIXED AXIS
Today s Objectives:
Students will be able to:
1. Analyze the planar kinetics
of a rigid body undergoing
rotational motion.
In-Class Activities:
Reading Quiz
Applications
Rotation Abou
Lecture #19 Part #1 MOMENT OF INERTIA
Today s Objectives:
Students will be able to:
1. Determine the mass moment
of inertia of a rigid body or a
system of rigid bodies.
In-Class Activities:
Reading Quiz
Applications
Mass Moment of Inertia
Parallel-Axi
Lecture #19 Part #1 MOMENT OF INERTIA
Today s Objectives:
Students will be able to:
1. Determine the mass moment
of inertia of a rigid body or a
system of rigid bodies.
In-Class Activities:
Reading Quiz
Applications
Mass Moment of Inertia
Parallel-Axi
Lecture #18 RELATIVE MOTION ANALYSIS:
Today s Objectives: ROTATING AXES
Students will be able to:
1. Resolve the acceleration of a point
using a rotating reference frame.
2. Determine the acceleration of a
points which are not located on the
same body.
In
Lecture #18 RELATIVE MOTION ANALYSIS:
Today s Objectives: ROTATING AXES
Students will be able to:
1. Resolve the acceleration of a point
using a rotating reference frame.
2. Determine the acceleration of a
points which are not located on the
same body.
In
Lecture #17 RELATIVE MOTION ANALYSIS:
Today s Objectives: ACCELERATION
Students will be able to:
1. Resolve the acceleration of a point
on a body into components of
translation and rotation.
2. Determine the acceleration of a
point on a body by using a re
Lecture #20 KINETIC ENERGY, WORK,
PRINCIPLE OF WORK AND ENERGY
Today s Objectives:
Students will be able to:
1. Define the various ways a force
and couple do work.
2. Apply the principle of work and
energy to a rigid body.
In-Class Activities:
Reading Qu
Lecture #20 KINETIC ENERGY, WORK,
PRINCIPLE OF WORK AND ENERGY
Today s Objectives:
Students will be able to:
1. Define the various ways a force
and couple do work.
2. Apply the principle of work and
energy to a rigid body.
In-Class Activities:
Reading Qu
Lecture #22 PLANAR KINETICS OF A RIGID
BODY: CONSERVATION OF ENERGY
Today s Objectives:
Students will be able to:
a) Determine the potential
energy of conservative forces.
b) Apply the principle of
conservation of energy.
In-Class Activities:
Reading Qui
Lecture #2 Part #1 CURVILINEAR MOTION:
GENERAL & RECTANGULAR COMPONENTS
Today s Objectives:
Students will be able to:
1. Describe the motion of a
particle traveling along a
curved path.
2. Relate kinematic quantities
in terms of the rectangular
components
Lecture #2 Part #1 CURVILINEAR MOTION:
GENERAL & RECTANGULAR COMPONENTS
Today s Objectives:
Students will be able to:
1. Describe the motion of a
particle traveling along a
curved path.
2. Relate kinematic quantities
in terms of the rectangular
components
CURVILINEAR MOTION:
NORMAL AND TANGENTIAL COMPONENTS
Today s Objectives:
Students will be able to:
1. Determine the normal and
tangential components of
velocity and acceleration of a
particle traveling along a
curved path.
In-Class Activities:
Reading Qu
CURVILINEAR MOTION:
NORMAL AND TANGENTIAL COMPONENTS
Today s Objectives:
Students will be able to:
1. Determine the normal and
tangential components of
velocity and acceleration of a
particle traveling along a
curved path.
In-Class Activities:
Reading Qu
Energy Norm Error Estimates
Mats G Larson
mgl@math.chalmers.se
Computational Mathematics,
and
Fraunhofer Centre for Industrial Mathematics
Computational Mathematics, and Fraunhofer Centre for Industrial Mathematics p.1
Outline
Residual based estimates
Loc
Chapter 5
Error Estimates for the Finite
Element Method
5.1
Introduction
In this chapter, we shall focus on two types of error estimates for the finite element method, a priori
and a posteriori estimates. (We have previously introduced these terms in the
Chapter 7
The finite element approximation
Pure mathematicians sometimes are satisfied with showing
that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result
as the only reasonable goal. Such o
Lecture #17 RELATIVE MOTION ANALYSIS:
Today s Objectives: ACCELERATION
Students will be able to:
1. Resolve the acceleration of a point
on a body into components of
translation and rotation.
2. Determine the acceleration of a
point on a body by using a re
Lecture #16 INSTANTANEOUS CENTER OF ZERO
VELOCITY
Today s Objectives:
Students will be able to:
1. Locate the instantaneous center of
zero velocity.
2. Use the instantaneous center to
determine the velocity of any point
on a rigid body in general plane
mo
Lecture #16 INSTANTANEOUS CENTER OF ZERO
VELOCITY
Today s Objectives:
Students will be able to:
1. Locate the instantaneous center of
zero velocity.
2. Use the instantaneous center to
determine the velocity of any point
on a rigid body in general plane
mo
THE WORK OF A FORCE, THE PRINCIPLE OF
WORK AND ENERGY & SYSTEMS OF PARTICLES
Today s Objectives:
Students will be able to:
1. Calculate the work of a force.
2. Apply the principle of work and
energy to a particle or system of
particles.
In-Class Activitie
EQUATIONS OF MOTION:
CYLINDRICAL COORDINATES
Today s Objectives:
Students will be able to:
1. Analyze the kinetics of a
particle using cylindrical
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equations of Motion Using
Cylindrical Coordin
EQUATIONS OF MOTION:
CYLINDRICAL COORDINATES
Today s Objectives:
Students will be able to:
1. Analyze the kinetics of a
particle using cylindrical
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equations of Motion Using
Cylindrical Coordin
EQUATIONS OF MOTION:
NORMAL AND TANGENTIAL COORDINATES
Today s Objectives:
Students will be able to:
1. Apply the equation of motion
using normal and tangential
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equation of Motion in n-t
Coord
EQUATIONS OF MOTION:
NORMAL AND TANGENTIAL COORDINATES
Today s Objectives:
Students will be able to:
1. Apply the equation of motion
using normal and tangential
coordinates.
In-Class Activities:
Reading Quiz
Applications
Equation of Motion in n-t
Coord
Lecture #5 Part #1 ABSOLUTE DEPENDENT MOTION
ANALYSIS OF TWO PARTICLES
Today s Objectives:
Students will be able to:
1. Relate the positions, velocities,
and accelerations of particles
undergoing dependent motion.
In-Class Activities:
Reading Quiz
Appli