In the lecture, the professor talk about three different ways to rotate so I was wondering are there any advantages for each of the ways?

Sicheng-Pan

In a given setting, one approach may be more intuitive than the rest. For instance, in flight simulations the Euler angles directly correspond to how the aircraft can be maneuvered in the sky.

Staffjamesfobrien

@Sicheng-Pan Exactly! Each is good in the right situation.

Put lots of math in your toolbox and you'll have the right tool for the job. If you don't have good math tools then it's sort of like a toolbox with jsut a hammer, screwdriver, and some tape: You can still do stuff but it will be hard and the results will be kludgy. If you have the right tools, things will be easier and you'll have nicer results.

(So many really good papers are: Someone had a good idea, but they tried to solve it with the wrong math and made a mess. Then someone else came along and just used the right math to produce a really elegant result that everyone uses and cites.)

In the lecture, the professor talk about three different ways to rotate so I was wondering are there any advantages for each of the ways?

In a given setting, one approach may be more intuitive than the rest. For instance, in flight simulations the Euler angles directly correspond to how the aircraft can be maneuvered in the sky.

@Sicheng-Pan Exactly! Each is good in the right situation.

Put lots of math in your toolbox and you'll have the right tool for the job. If you don't have good math tools then it's sort of like a toolbox with jsut a hammer, screwdriver, and some tape: You can still do stuff but it will be hard and the results will be kludgy. If you have the right tools, things will be easier and you'll have nicer results.

(So many really good papers are: Someone had a good idea, but they tried to solve it with the wrong math and made a mess. Then someone else came along and just used the right math to produce a really elegant result that everyone uses and cites.)