### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# PHYS608 PHYS608

SDSU

GPA 3.75

### View Full Document

## 20

## 0

## Popular in Course

## Popular in Physics 2

This 27 page Class Notes was uploaded by Citlalli Sauer on Tuesday October 20, 2015. The Class Notes belongs to PHYS608 at San Diego State University taught by M.Bromley in Fall. Since its upload, it has received 20 views. For similar materials see /class/225318/phys608-san-diego-state-university in Physics 2 at San Diego State University.

## Popular in Physics 2

## Reviews for PHYS608

### What is Karma?

#### Karma is the currency of StudySoup.

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

Date Created: 10/20/15

Lecture 4 Outline Show us ya Lagrange a new D Alembert s principle Section 14 o Lagrange s Equation Section 14 o and some examples Section 16 Reversed effective force I 0 last time D Aleinbert s principle and generalised Force a d d o expanding the 2nd reversed effective Force term d z s dZ s dZ 377 i i j i 0 again distributive b b 61 a i 5 73 mi 1 1dt239aqjdt Zdt39aqj zdzt39dt aqj 0 chain rule the 2nd right hand term of Eq1 1aa8 2 Z ni 4 dt dqj an k 3an at 593015 861739 Reversed effective force II 0 now for the rst of the right hand terms of Eq1 aaacf am 8z7 0 thus we simplify the reversed effective force term d cm 37 57 i 5 39 2 dt r m dig 8 qj Z i mg 5 ji dt 1 zaqj z raqj Q7 D Alembert s Principle Take II 0 So now reversing such that 0 d 677 o and simplifying reversed effective and generalised forces d 827 827 fin z 5 0 gt maqj Q1 d a use 2amp6 EL EL i52 0n the rst two terms 13 d3 13 d a 1 2 a 1 i2 1 7 z z 5 0 dt 327 aqj 2mlvl C17 1 M j 0 but T m z7 2 gives new D Alei nbert s Principle d 8T 8T 5 0 Z idt adj 3613 M Q j D Alembert s Independence 7 7 39 39 d z39 original D Alembert s Prlnmple ft ua0 and the new form of D Alembert s Principle d 8T 8T 5 0 7 dt adj 3617 Q7 Q If the qj are linearly independent ie holonomic ie Zj chj 0 iff all cj 0 then 1 61 8TQ dt j with n equations for each generalised coordinate in Cartesian co ords 3 0 since no curvature 7 Easy Examples free particle contd free particle in polar coords I free particle in polar coords I Lagrange s Equations 39 i 7 M 39 39 i lt9T lt9T o holononnc D Alernbeit s PrinCiple dt adj aqj Q7 0 when the generalised Forces are Fi V V then a a a 37 av Q 1 ViV 1 j Z Z L o The last step can be seen by simple example Thus age Wa m LW 0 assuming that V is independent of time conservative 1 a a 0 a note that L T V is not the only choice of Lagrangian Simple vector calculus example Prescription a Can we de ne a Lagrangian ie Holonomic system a with applied forces derivable from ordinary or a generalised potential 0 and workless constraints 1 Write T and V in generalised coordinates 2 Form 3 from T V 3 Get equations of motion in each coordinate j from 1 a a 0 a transforming T from eg Cartesian into generalised coordinates is generally the hardest bit potential problem Cartesian Lecture 4 Outline Show us ya Lagrange a new D Alembert s principle Section 14 o Lagrange s Equation Section 14 o and some examples Section 16 Reversed effective force I 0 last time D Aleinbert s principle and generalised Force a d d o expanding the 2nd reversed effective Force term d z s dZ s dZ 377 i i j i 0 again distributive b b 61 a i 5 73 mi 1 1dt239aqjdt Zdt39aqj zdzt39dt aqj 0 chain rule the 2nd right hand term of Eq1 1aa8 2 Z ni 4 dt dqj an k 3an at 593015 861739 Reversed effective force II 0 now for the rst of the right hand terms of Eq1 aaacf am 8z7 0 thus we simplify the reversed effective force term d cm 37 57 i 5 39 2 dt r m dig 8 qj Z i mg 5 ji dt 1 zaqj z raqj Q7 D Alembert s Principle Take II 0 So now reversing such that 0 d 677 o and simplifying reversed effective and generalised forces d 827 827 fin z 5 0 gt maqj Q1 d a use 2amp6 EL EL i52 0n the rst two terms 13 d3 13 d a 1 2 a 1 i2 1 7 z z 5 0 dt 327 aqj 2mlvl C17 1 M j 0 but T m z7 2 gives new D Alei nbert s Principle d 8T 8T 5 0 Z idt adj 3613 M Q j D Alembert s Independence 7 7 39 39 d z39 original D Alembert s Prlnmple ft ua0 and the new form of D Alembert s Principle d 8T 8T 5 0 7 dt adj 3617 Q7 Q If the qj are linearly independent ie holonomic ie Zj chj 0 iff all cj 0 then 1 61 8TQ dt j with n equations for each generalised coordinate in Cartesian co ords 3 0 since no curvature 7 Easy Examples free particle free particle in polar coords I free particle in polar coords II Lagrange s Equations 39 i 7 M 39 39 i lt9T lt9T o holononnc D Alernbeit s PrinCiple dt adj aqj Q7 0 when the generalised Forces are Fi V V then a a a 37 av Q 1 ViV 1 j Z Z L o The last step can be seen by simple example Thus age Wa m LW 0 assuming that V is independent of time conservative 1 a a 0 a note that L T V is not the only choice of Lagrangian Simple vector calculus example Prescription a Can we de ne a Lagrangian ie Holonomic system a with applied forces derivable from ordinary or a generalised potential 0 and workless constraints 1 Write T and V in generalised coordinates 2 Form 3 from T V 3 Get equations of motion in each coordinate j from 1 a a 0 a transforming T from eg Cartesian into generalised coordinates is generally the hardest bit Space potential problem Cartesian potential problem Polar

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

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

#### "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!"

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "Their 'Elite Notetakers' are making over $1,200/month in sales by creating high quality content that helps their classmates in a time of need."

### 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

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.