A spherical object can rotate in any dimension, but what about an asymmetric object?
To illustrate this, think of a pen or pencil inclined at 45 degrees to the y-axis. If we apply an external torque we can get it to rotate about the y-axis (i.e. at 45 degrees to its long axis). But if we remove the external torque, will it continue to rotate in this way?
In the interests of science, I have been experimenting an throwing pens in the air. I cant get it to rotate in this way, as soon as it leaves my hand it just wants to rotate about its short axis (i.e. with the pointed end and the erazor on the outside of the spin).
I can get the pen to spin about its short axis or its long axis, but not in-between.
I think I can get it to spin about both these axies at the same time (its difficult to be sure as my eyes aren't fast enough). but what appears to be happening is that it is rotating pointed end over erazor, and then it is spinning about its long axis which is rotating itself. So it appears to be making a complex rotation, as described above, of a rotation within a rotation.
So what are the allowed modes of rotation for any object?
Some answers from Yaakov Eisenberg, thank you for this - Martin :
> What if it were being forced to rotate in this direction and then
Yes, it would instantly start to rotate about a different axis, but the change is not as discontinuous (therefore, unrealistic) as it might seem. The velocities of the masses change continuously; only their accelerations change discontinuously, due to the discontinuous change in the force.
> So given a generalised inertia matrix, what are the conditions for
When rotating about the axis, the object's angular momentum vector must be parallel to the axis (i.e., parallel to the object's angular velocity vector). If this is the case, the axis of rotation will remain constant in time. Otherwise, it won't.
For any object, there are at least three axes for which this is true. They are called the object's principal axes, and the inertia matrix is diagonal in the coordinate system defined by them. If the object is sufficiently symmetric, there will be more than three.
> Is it that single rigid object
I think this is also a correct way of stating it.
|Correspondence about this page|
Book Shop - Further reading.
Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.
Game Physics - This book has some useful stuff, its more of a textbook, not a step by step guide (although it does have a disc with a lot of C++ code). About the first third of the book is a physics textbook with theoretical exercises, the middle bit covers physics engine topics, and the last third of the book covers mathematical topics. I think I would use this book as a reference book to lookup the theory behind something I might be working on rather than a book to work through in order.
Commercial Software Shop
Where I can, I have put links to Amazon for commercial software, not directly related to the software project, but related to the subject being discussed, click on the appropriate country flag to get more details of the software or to buy it from them.
This site may have errors. Don't use for critical systems.