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    Welcome Back To 8.033!: Leonhard Euler, Swiss, 1707-1783

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    Welcome Back To 8.033!: Leonhard Euler, Swiss, 1707-1783

    Uploaded by

    Utkarsh Verma
    12 views8 pages
    hjbjhb

    Original Title

    Lecture8 Euler

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    12 views8 pages

    Welcome Back To 8.033!: Leonhard Euler, Swiss, 1707-1783

    Uploaded by

    Utkarsh Verma
    hjbjhb

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 8

    Welcome

    back
    to 8.033!
    Leonhard Euler, Swiss, 1707-1783

    Image Courtesy of Wikipedia

    Summary of course so far: See study guide


    Main focus: be able to solve problems
    that involve converting between
    different inertial frames

    MIT Course 8.033, Fall 2006, Lecture 8


    Max Tegmark

    Today: Geodesics, calculus of variations


    The Euler-Lagrange equation
    Deriving it
    Using it:
    - metrics, Euclidean space geodesics
    - Minkowski space geodesics
    - gravitational redshift
    - brachistochrone problem
    -caternary

    Photograph of a brachistochrone experiment. Image removed due to copyright restrictions.

    Brachistochrone flicks

    Vertical fall (ft)

    Flat board
    T = 3.54 sec

    Cycloid
    T = 3.23 sec
    Y

    ds2 = dx2 + dy2

    Circular arc
    T = 3.23 sec
    100

    g0

    X
    Horizontal displacement (ft)

    100

    Figure by MIT OCW.

    c=1

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