NTNUJAVA Virtual Physics Laboratory
Enjoy the fun of physics with simulations!
Backup site http://enjoy.phy.ntnu.edu.tw/ntnujava/
February 28, 2021, 11:29:32 am *
Welcome, Guest. Please login or register.
Did you miss your activation email?

Login with username, password and session length
   Home   Help Search Login Register  
Use resources around us effectively. ...Wisdom
Google Bookmarks Yahoo My Web MSN Live Netscape Del.icio.us FURL Stumble Upon Delirious Ask FaceBook

Pages: [1]   Go Down
Author Topic: FREE ROTATION OF AN AXIALLY SYMMETRICAL BODY (Eugene Butikov)  (Read 10368 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).
Fu-Kwun Hwang
Hero Member
Offline Offline

Posts: 3086

Embed this message
on: October 21, 2007, 12:18:24 pm »


You can make a pause in the simulation and resume it by clicking on the button "Start/Pause" on the control panel located on the left-hand side of the applet window. This control panel allows you also to vary parameters of the system and conditions of the simulation. By dragging the pointer of the mouse inside the applet window (moving the pointer with the left button pressed) you can rotate the image around the vertical and horizontal axes for a more convenient point of view.

The vector of angular velocity (the yellow arrow on the black background) shows in space the direction of momentary axis of rotation. The set of these momentary axes at different moments of time forms in space a circular cone whose vertex is located at the center of mass and whose axis is directed along vector L of the angular momentum (vertically on the screen). This space cone is also called the immovable axoid (see the right-hand side of the applet window).

Next we imagine one more circular cone, this time attached firmly to the body. The vertex of this cone is also located at the center of mass, and its axis is directed along the axis of symmetry of the body. Let the generator of this cone be the vector of angular velocity ω (the yellow arrow on the screen), that is, the momentary axis of rotation. In other words, the lateral surface of this cone associated with the body is formed by the set of momentary axes of rotation at different moments of time, and shows how these axes are located inside the body (relative to the body). For this reason, this imaginary cone, associated with the rotating body, is called the moving axoid (or the body cone).

The moving and immovable cones touch one another (outwardly for a prolate body, whose transverse moment of inertia is greater than longitudinal) by their lateral surfaces along vector ω that shows the momentary axis of rotation. All the points of the body, which are located at a given moment of time on the momentary axis of rotation, have zero linear velocities. This means that the moving cone (attached to the body) is just rolling without slipping over the surface of the immovable cone. This clear geometrical interpretation of kinematics of the free precession (of the inertial rotation) is shown in the right-hand side of the applet.
Pages: [1]   Go Up
Use resources around us effectively. ...Wisdom
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Free Oscillations and Rotations of a Rigid Pendulum by Eugene Butikov
Ejs simulations from other web sites
Fu-Kwun Hwang 2 24037 Last post January 06, 2009, 08:32:35 pm
by Fu-Kwun Hwang
Ejs simulations from other web sites
Fu-Kwun Hwang 1 16290 Last post April 01, 2010, 07:49:03 am
by lookang
Restricted three-body problem – a satellite in the binary planet system (Eugene)
Ejs simulations from other web sites
Fu-Kwun Hwang 0 13500 Last post October 21, 2007, 07:48:35 pm
by Fu-Kwun Hwang
Rotation in 3D (Does the order of rotation matter?)
Fu-Kwun Hwang 0 9032 Last post February 07, 2010, 03:49:45 pm
by Fu-Kwun Hwang
Rotation in 3D (Does the order of rotation matter?)
ahmedelshfie 0 13727 Last post May 21, 2010, 01:46:52 am
by ahmedelshfie
Powered by MySQL Powered by PHP Powered by SMF 1.1.13 | SMF © 2006-2011, Simple Machines LLC Valid XHTML 1.0! Valid CSS!
Page created in 0.049 seconds with 22 queries.since 2011/06/15