Tutorial Exercises: Lagrangian Dynamics
1. Practise at solving differential equations
Write down the Euler-Lagrange equations associated with the following Lagrangian L(t, x, y, x,
y):
(a) x 2 + y 2 k 2 (x + y)2
(b) x 2 + y 2 k 2 (x y)2
(c) x 2 + y 2 + k
How do you design a hovercraft?
Todays step:
1. Define and clarify
the problem
(Chp 21, 22.6)
[Source: Kosky, Chp 19.8]
Specifications
Where do specifications come from?
Analyzing the requirements
Modeling the behavior of your system
Example: NASA Mars
How do you design a hovercraft?
Todays step:
1. Define and clarify
the problem
(Chp 21, 22.6)
[Source: Kosky, Chp 19.8]
Specifications
Where do specifications come from?
Analyzing the requirements
Modeling the behavior of your system
Determining an obje
How do you design a hovercraft?
Problem definition
Requirements -> Specifications: basic mechanics
Design options / concepts
Simulation to better understand each option/concept
Setting up 2D motion simulations
Setting up double-integrator simulations
How do you design a hovercraft?
Problem definition
Requirements -> Specifications: basic mechanics
Design options / concepts
Simulation to better understand each option/concept
2D motion simulations
Fluid mechanics (1D and 2D flow)
Data sheets
Decis
Steps in the Engineering Design
Process
1. Define the problem
2. Generate alternative
concepts
3. Evaluate and select a
concept
4. Detailed design
5. Design defence / review
6. Manufacturing and
testing
7. Performance evaluation
8. Final design report
[So
ENGR 290 Introductory Engineering Team Design Project (3 credits)
Course Outline for Fall 2016
Lectures: Tuesdays and Thursdays 4:15-5:30pm,
MB 2.430 SGW
Instructor: Dr. Krzysztof (Chris) Skonieczny, Assistant Professor, Electrical and Computer
Engineerin
How do you design a hovercraft?
As part of a team! [Chp 20.3]
By following a schedule [Chp 20.2]
By following the steps in the Engineering
Design Process
How do you design a hovercraft?
As part of a team! [Chp 20.3]
By following a schedule [Chp 20.2]
ENGR 290
Introductory Engineering Team Design Project
Taught by Krzysztof (Chris) Skonieczny
What is engineering design?
The process of creating things that meet certain
requirements and perform specific functions
A form of problem solving
Some common pro
How do you design a hovercraft?
Problem definition
Requirements -> Specifications: basic mechanics
Design options / concepts
Simulation to better understand each option/concept
2D motion simulations
Fluid mechanics
Data sheets
Decision matrix
Types
Due October 22nd 2015
Solution Homework 5
Q1)
The volumetric flow rate, Q , of a flow of water through a horizontal pipe is 0.05 m3 /s.
Determine the velocity of flow at a point where the diameter of the pipe is (a) 0.1 m, (b) 0.05 m
1 = 2 =
4
1
1
4
2
2
How do you design a hovercraft?
1. Define the problem
2. Generate alternative
concepts
3. Evaluate and select a
concept
4. Detailed design
5. Design defence / review
6. Manufacturing and
testing
7. Performance evaluation
8. Final design report
[Source: Ko
Assignment 1
3 questions on 1 page
total 50 marks
5% of final grade
Due: Oct 4, 2016, 4:15pm (at start of lecture)
This is an individual assignment. Please submit with an Expectations of Originality form.
NOTE: The questions in this assignment are meant t
Miniquiz O
1. Write the components of the vector F expressed in the:
mgb F=I Flo? '
IFlanqa
F = F H: (9 "' f)
I F! Mn ( 9 + 9)
If you need to review vectors and reference frames, you may nd the following links useful:
A basic overview: http:/www.u
Homework 4 Due Oct 6 (at start of lecture)
Each question must be honestly attempted in order for your Quiz 4 grade to count
4 questions on 2 pages
Q1) Hand in a copy of the minutes and attachments from a group meeting. The agenda for this
meeting is given
1. i) A: The telephone shall withstand temperatures up to 60 oC. B: The telephone shall withstand
temperatures up to 25 oC.
A is better. B is not sufficient: the customer, a telephone user, very often needs their telephone to work
at temperatures above 25
Evolution of a robot design
Chris Skonieczny
ENGR 290
Steps in the Engineering Design
Process
1. Define the problem
2. Generate alternative
concepts
3. Evaluate and select a
concept
4. Detailed design
5. Design defence / review
6. Manufacturing and
testin
Find (&
perhaps build)
something
that satisfies
requirements
y1, y2, y3, etc.
Given parts &
components
x1, x2, x3, etc.
Design
process
something,
(i.e. a system)
How well does it
satisfy the
requirements?
How do you design a hovercraft?
Todays step:
1. De
Solved Problems in Mechanics
Problem 1: (Using SI units)
You pull a hovercraft with a force of 50 N along a sandbar that is 5 m long. How much work is
done on the hovercraft?
Solution:
The work done is equal to the force applied times the distance it acts
ENGR 290 - Problems Set #2
1.
a) (1 mark) Calculate the moment of inertia, I, for free rotations of the hovercraft shown below. Note
that the center of mass is located at the center of the lift fan.
b) (1 mark) Fthrust = 1 N. Calculate the instantaneous l
Problems in Mechanics
Problem 1: (Using SI units) You pull a hovercraft with a force of 50 N along a sandbar that is 5
m long. How much work is done on the hovercraft?
Problem 2: (Using Imperial units) Your hovercraft weighs 60 lb and is sitting on the fl
ENGR 290 Homework #1
Draw free-body diagrams for the listed objects:
2.
m1
a) m1 assuming a smooth surface (i.e. neglect friction)
b) m1 assuming a rough surface (i.e. with friction)
m2 m3
c) m2 assuming a smooth surface
d) m3 assuming a smooth surface
3.
ENGR 290 Introductory Engineering Team Design Project (3 credits)
Course Outline for the Winter 2016
Lectures: Wednesday and Friday - 10:15-11:30 am
Instructor: Dr. K. Khorasani, Professor, Dept. of Electrical and Computer Engineering
Contact: [email protected]
Pressure and Fluid Statics
1
Mechanics
The study of object properties that relate to the dimensions of
distance or length [L], mass [M], and time [T]
Quantity
Units (SI)
Dimension
Displacement, distance, length
m
[L]
Area
m2
[L2]
Volume
m3
[L3]
Mass
kg
[M
Fluid Statics (Part B)
1
Outline
Overview
Pressure at a Point
Basic Equations for the Pressure Field
Hydrostatic Condition
Measurement of Pressure
2
Pressure at a Point: Pascals Law
Blaise Pascal (1623-1662)
Pressure is the normal force per unit area at a
Rigid Bodies:
Equivalent Systems of Forces
Introduction
Most bodies in elementary mechanics are assumed to be rigid, i.e., the
actual deformations are small and do not affect the conditions of
equilibrium or motion of the body.
Current note describes th
Design Process
1
What is Design?
The word design is often used as a
generic term that refers to anything that
was made by conscious human effort.
It is the creative process of turning
abstract ideas into physical
representation such as products and
system
Analytic Hierarchy Process
Objectives
1.
2.
3.
Use the multifactor evaluation process in making
decisions that involve a number of factors, where
importance weights can be assigned.
Understand the use of the analytic hierarchy process
in decision making.
Objectives:
1) Introduction to analysis and design of physical systems
2) System Classification
1) Introduction to analysis and design of physical systems
a) Performance Specification
b) Modeling
A tool for study, analysis, and design
A representation o
Distributed Forces:
Centroids and Centers of Gravity
Introduction
The earth exerts a gravitational force on each of the particles
forming a body. These forces can be replace by a single
equivalent force equal to the weight of the body and applied
at the