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10/24/2014PHY 711 Fall 2014 -- Lecture 251 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 25: Rotational.

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Presentation on theme: "10/24/2014PHY 711 Fall 2014 -- Lecture 251 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 25: Rotational."— Presentation transcript:

1 10/24/2014PHY 711 Fall 2014 -- Lecture 251 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 25: Rotational motion (Chapter 5) 1.Rigid body motion in body fixed frame 2.Conversion between body and inertial reference frames

2 10/24/2014PHY 711 Fall 2014 -- Lecture 252

3 10/24/2014PHY 711 Fall 2014 -- Lecture 253 r  Summary of previous results describing rigid bodies rotating about a fixed origin

4 10/24/2014PHY 711 Fall 2014 -- Lecture 254 Moment of inertia tensor

5 10/24/2014PHY 711 Fall 2014 -- Lecture 255 r  Summary of previous results describing rigid bodies rotating about a fixed origin

6 10/24/2014PHY 711 Fall 2014 -- Lecture 256 Descriptions of rotation about a given origin -- continued

7 10/24/2014PHY 711 Fall 2014 -- Lecture 257 Descriptions of rotation about a given origin -- continued

8 10/24/2014PHY 711 Fall 2014 -- Lecture 258

9 10/24/2014PHY 711 Fall 2014 -- Lecture 259 Solution of Euler equations for a symmetric top -- continued

10 10/24/2014PHY 711 Fall 2014 -- Lecture 2510

11 10/24/2014PHY 711 Fall 2014 -- Lecture 2511 Euler equations for asymmetric top -- continued

12 10/24/2014PHY 711 Fall 2014 -- Lecture 2512 Transformation between body-fixed and inertial coordinate systems – Euler angles http://en.wikipedia.org/wiki/Euler_angles inertial body y x y x

13 10/24/2014PHY 711 Fall 2014 -- Lecture 2513 y x y x Need to express all components in body-fixed frame:

14 10/24/2014PHY 711 Fall 2014 -- Lecture 2514 y x y x

15 10/24/2014PHY 711 Fall 2014 -- Lecture 2515

16 10/24/2014PHY 711 Fall 2014 -- Lecture 2516

17 10/24/2014PHY 711 Fall 2014 -- Lecture 2517 y x y x

18 10/24/2014PHY 711 Fall 2014 -- Lecture 2518 Rotational kinetic energy

19 10/24/2014PHY 711 Fall 2014 -- Lecture 2519 Transformation between body-fixed and inertial coordinate systems – Euler angles http://en.wikipedia.org/wiki/Euler_angles inertial body y x y x

20 10/24/2014PHY 711 Fall 2014 -- Lecture 2520 General transformation between rotated coordinates – Euler angles http://en.wikipedia.org/wiki/Euler_angles inertial body y x y x

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