In lecture you mentioned that rotation has 3 degrees of freedom. Could you explain this? I thought the only variable was theta.
mpotoole
In 2D space, you are absolutely correct: there is only 1 degree of freedom for rotation in 2D space.
In 3D space, we can rotate objects around 3 different axis: the x-, y-, or z- axis. Any arbitrary rotation can be described in terms of three separate rotation operations, one around each of these axis. Therefore, there are 3 degrees of freedom in this case.
In lecture you mentioned that rotation has 3 degrees of freedom. Could you explain this? I thought the only variable was theta.
In 2D space, you are absolutely correct: there is only 1 degree of freedom for rotation in 2D space.
In 3D space, we can rotate objects around 3 different axis: the x-, y-, or z- axis. Any arbitrary rotation can be described in terms of three separate rotation operations, one around each of these axis. Therefore, there are 3 degrees of freedom in this case.