Still confused why we must have three degrees of freedom... Can someone explain?
sccao
This makes sense, but is not intuitive. I'm curious as to why this is so not intuitive.
jasonx
This is a confusing slide. Rotation about a fixed center in 2D only requires an angle, and rotation about a fixed normal in 3D only requires an angle.
This is distinct from representing points using polar coordinates in 2D and spherical coordinates in 3D.
meranara
Are we not always rotating about a fixed center (the origin)?
Parker
@yee We need three degrees to allow the globe to rotate while a city is fixed. We can rotate Pittsburgh to any other city with two degrees - longitude and latitude, but we can't rotate around Pittsburgh. Imagine spinning a basketball on your finger, where your basketball is Earth and your finger is Pittsburgh. There's no way to express that without a third degree of freedom.
@meranara I think we are always rotating around the origin, yes. I think what Jason means is the direction of rotation being expressed by a normal vector or axis at the origin. In the basketball spinning example, the direction of your finger is the fixed normal you rotate around.
Still confused why we must have three degrees of freedom... Can someone explain?
This makes sense, but is not intuitive. I'm curious as to why this is so not intuitive.
This is a confusing slide. Rotation about a fixed center in 2D only requires an angle, and rotation about a fixed normal in 3D only requires an angle.
This is distinct from representing points using polar coordinates in 2D and spherical coordinates in 3D.
Are we not always rotating about a fixed center (the origin)?
@yee We need three degrees to allow the globe to rotate while a city is fixed. We can rotate Pittsburgh to any other city with two degrees - longitude and latitude, but we can't rotate around Pittsburgh. Imagine spinning a basketball on your finger, where your basketball is Earth and your finger is Pittsburgh. There's no way to express that without a third degree of freedom.
@meranara I think we are always rotating around the origin, yes. I think what Jason means is the direction of rotation being expressed by a normal vector or axis at the origin. In the basketball spinning example, the direction of your finger is the fixed normal you rotate around.