×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

## Mechanical and Aerospace Engineering Laboratory

by: Vinnie Hansen V

70

0

20

# Mechanical and Aerospace Engineering Laboratory MAE 315

Marketplace > Syracuse University > Engineering Mechanical & Aero > MAE 315 > Mechanical and Aerospace Engineering Laboratory
Vinnie Hansen V
Syracuse
GPA 3.51

Mark Glauser

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
Mark Glauser
TYPE
Class Notes
PAGES
20
WORDS
KARMA
25 ?

## Popular in Engineering Mechanical & Aero

This 20 page Class Notes was uploaded by Vinnie Hansen V on Wednesday October 21, 2015. The Class Notes belongs to MAE 315 at Syracuse University taught by Mark Glauser in Fall. Since its upload, it has received 70 views. For similar materials see /class/225608/mae-315-syracuse-university in Engineering Mechanical & Aero at Syracuse University.

×

## Reviews for Mechanical and Aerospace Engineering Laboratory

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/21/15
Underdetermined and Overdetermined Linear Algebraic Systems ESlOO March 1 1999 TS Whitten Objectives 0 De ne underdetermined systems 0 De ne overdetermined systems 0 Least Squares Examples Review SOON 2Fx20 500 FBCsin45020 sz 0 FBC cos4SO FBA 0 sin45O O FBC 500 005450 1 FBA O V coe icz ents variables Review cont sin45O O FgC 500 cos45O l 5amp4 O x V J E coe icienis variables The system of matrices above is of the form AX b and can be solved using MATLAB left division thus x Ab results in a lgtlt2 matrix of values for F BC and F B A Review Summary 0 A system of two Equations and two unknowns may yield a unique solution 0 The exception is when the determinant of A is equal to zero Then the system is said to be singular 0 The left division operator will solve the linear system in one step by combining two matrix operations OAB is equivalent to A391B Graphical Representation of Unique vs Singular Systems I unique solution I y singular system Underdetermined Systems 0 A system of linear equations is may be undetermined if 1 The determinant of A is equal to zero A 0 2 The matrix A is not square ie the are more unknowns than there are equations X3y2Z22 1 3 2 x 2 xyZ4 1 1 li39y 4 Z Overdetermined Systems 0 The converse of an underdetermined system is an overdetermined system Where there are more equations than there are variables 0 This situation arises frequently in engineering For example suppose a linear relationship is expected between x and y and there are multiple data points Data Distribution of Linear Phenomena A experimental data Data Distribution of Linear Phenomena A experimental data ymxb The line y mx b that best describes this data is Obtained by the method ofleast squares Method of Least Squares xpyl The line that results in the minimum value of J is the least squares linear t to the data 25 20 15 Y 10 Example 0 data linear t 5 10 15 LOOJNOUO lFOONAIH O data 300 316 566 815 1184 1385 1488 1767 1653 2165 The Overdetermined System 0 Once the curve t is obtained a y value may be interpolated for any xvalue Within the x data range sometimes extrapolation is possible 0 In the following example fmins is used to minimize the sum of the squared residuals with respect to the slope and intercept Flowchart for leastrn load datatxt J calculate line assign columns 4 plot i line call fmins l assign output plot data points 4 and line generate X vector Run leastm Solving The Overdetermined System Method 11 0 Solving the overdetermined system is carried out the same way as the other linear algebra solutions using the left division method m x AB b Method 11 cont d 0 If the system is not overdetermined the method will not work Overdetermined system cont 1mb300 data 1 300 5mb1184 2 316 3 566 10mb2165 4 815 5 1184 6 1385 1 300 2 1312 m 9 1653 5 1 b 1184 10 2165 10 1 2165 A X B Program least2m Load the data Build matrix A Build matrix b Print slope intercept Generate X y pairs using fit Left diVide parametersAB Plot data and titgenerated Xy set Run leasth

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Steve Martinelli UC Los Angeles

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Anthony Lee UC Santa Barbara

#### "I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com