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 Exercise 12.1 - 5 not 6? 
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Joined: 18 Mar 2008, 02:04
Posts: 1
Post Exercise 12.1 - 5 not 6?
Exercise 12.1 asks to explain more explicitly why the dimension of the configuration space for a rigid body in Euclidean 3-space is 6. As specified it seems to me that the correct dimension is 5. Why? There are 3 dimensions needed to specify the location of the center of mass of the rigid body and only two spherical coordinates to specify the orientation of the body assuming that a canonical orientation for the body has been chosen. There is no need for a radial component since all that is being specified is the direction the body is pointing and no magnitude of any sort related to that direction - such as for example speed of rotation.

What am I missing?

18 Mar 2008, 02:17
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Joined: 25 Feb 2008, 13:32
Posts: 106
Location: Cape Town, South Africa
Post Re: Exercise 12.1 - 5 not 6?
What about the extra degree of freedom needed to account for rotation about the line through the origin?

Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there.

19 Mar 2008, 02:46
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