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 transcript:

10/24/2014PHY 711 Fall 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

10/24/2014PHY 711 Fall Lecture 252

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

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

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

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

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

10/24/2014PHY 711 Fall Lecture 258

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

10/24/2014PHY 711 Fall Lecture 2510

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

10/24/2014PHY 711 Fall Lecture 2512 Transformation between body-fixed and inertial coordinate systems – Euler angles inertial body y x y x

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

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

10/24/2014PHY 711 Fall Lecture 2515

10/24/2014PHY 711 Fall Lecture 2516

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

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

10/24/2014PHY 711 Fall Lecture 2519 Transformation between body-fixed and inertial coordinate systems – Euler angles inertial body y x y x

10/24/2014PHY 711 Fall Lecture 2520 General transformation between rotated coordinates – Euler angles inertial body y x y x

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