This was extremely helpful. You should make a lecture walking through the biomechanics application of this (joint angles vs joint angular velocities). This would be helpful to people like myself and the person below with the baseball bat application. It is pretty common for kinesiology majors to end up in biomechanics programs and we tend to have significantly lesser mathematical backgrounds than engineers and not many programs address the progression from 2-D to 3-D, which is far less straight forward than some lead us to believe. Videos like this help a lot as we sort through the math of it all!
What Schaub & Junkins call a constraint sphere is actually the glome that describes the 4D spacetime of the system. The full set of rotations is SO(4) Lie group. For quantum mechanics (spin) you use Cayley-Klein parameters instead of Euler-Rodrigues parameters. The SO(4) group when applied to spacetime gives the geodesic equation of general relativity including the Christoffel symbols and space curvature aka Riemann and Ricci tensors. The gradient of the spacetime quaternion gives directly the Maxwell equaions (the commutator is the magnetic field and the anticommutator is the electric field). This derivation of Maxwell equations gives also a third field which is variously called scalar field or temporal field. This field has been investigated for biological activity (it slows the nerve impulses by about 7%) and there are some proposed uses for military applications (e.g, anti-submarine war).
I’m trying to compute the Euler angles of a baseball bat swing from xyz time series marker data. Any suggestions on how to go about calculating this? I don’t have an engineering background
Wow, that's kind of a cool problem. If you've got xyz data for multiple points on the bat, then that is enough to do what you need to do. I don't know if there's an 'off the shelf' package you can use, but you might Google it. I think I know what I would do, but it's complicated to describe. If you'd like help, email me.
Problem with Euler angles 1.weird matrix 2.unique orientation is not uniquely described by euler angles. ok but what about Gimbal lock. Assume rotation ZXY they say Z is child of X and X is child of Y and when X rotates by 90 degree why should gimbal Z rotate and orient with gimbal Y and faces gimbal lock. Is it Linked to Your explanation... I Mean to ask you is there any link between Problem with Euler angles and Gimbal Lock , if so my 2nd question holds what about Gimbal lock in 2nd line of comment....
Hello there, I’m taking classical dynamics course and your videos are so great. I’m considering PhD in ME(Dynamics and controls). I assume you’re an advisor for PhD students. How soon your students finish their PhD? The shortest and longest. Thank you so much for your videos.
Thanks so much for watching the videos and sharing! Shortest time to PhD was 3 years (the minimum necessary, student had a MS already) and longest was 6 or 7 years. The average is 4.5 years. There's a list of my graduated PhD students in my CV www.dept.aoe.vt.edu/~sdross/Ross_CV.pdf
The most cutest professor i have ever seen in my life.. haha 🎀
Thanks a lot for the lectures btw.
Best explanation for angular velocity and Euler angle I have ever seen in RUclips, Respect!
Thank you so much, Wenyang!
@@ProfessorRoss the name of the book please . Thank you so much
This was extremely helpful. You should make a lecture walking through the biomechanics application of this (joint angles vs joint angular velocities). This would be helpful to people like myself and the person below with the baseball bat application. It is pretty common for kinesiology majors to end up in biomechanics programs and we tend to have significantly lesser mathematical backgrounds than engineers and not many programs address the progression from 2-D to 3-D, which is far less straight forward than some lead us to believe. Videos like this help a lot as we sort through the math of it all!
What Schaub & Junkins call a constraint sphere is actually the glome that describes the 4D spacetime of the system. The full set of rotations is SO(4) Lie group. For quantum mechanics (spin) you use Cayley-Klein parameters instead of Euler-Rodrigues parameters. The SO(4) group when applied to spacetime gives the geodesic equation of general relativity including the Christoffel symbols and space curvature aka Riemann and Ricci tensors. The gradient of the spacetime quaternion gives directly the Maxwell equaions (the commutator is the magnetic field and the anticommutator is the electric field). This derivation of Maxwell equations gives also a third field which is variously called scalar field or temporal field. This field has been investigated for biological activity (it slows the nerve impulses by about 7%) and there are some proposed uses for military applications (e.g, anti-submarine war).
What about when finding the second derivative/ angular accelerations is it the same?
I’m trying to compute the Euler angles of a baseball bat swing from xyz time series marker data. Any suggestions on how to go about calculating this? I don’t have an engineering background
Wow, that's kind of a cool problem. If you've got xyz data for multiple points on the bat, then that is enough to do what you need to do. I don't know if there's an 'off the shelf' package you can use, but you might Google it. I think I know what I would do, but it's complicated to describe. If you'd like help, email me.
Guess it's time to change my Intel biomechanics Lab Co-op Internship technical interview exercise!!!! hahah
31:04 is the equation we want.
Problem with Euler angles 1.weird matrix 2.unique orientation is not uniquely described by euler angles.
ok but what about Gimbal lock. Assume rotation ZXY they say Z is child of X and X is child of Y and when X rotates by 90 degree why should gimbal Z rotate and orient with gimbal Y and faces gimbal lock. Is it Linked to Your explanation... I Mean to ask you is there any link between Problem with Euler angles and Gimbal Lock , if so my 2nd question holds what about Gimbal lock in 2nd line of comment....
Sir from which book you teach?
I use this book, Schaub & Junkins, Analytical Mechanics of Space Systems, 4th edition, 2018, arc.aiaa.org/doi/book/10.2514/4.105210
Thankyou
Hello there, I’m taking classical dynamics course and your videos are so great. I’m considering PhD in ME(Dynamics and controls). I assume you’re an advisor for PhD students. How soon your students finish their PhD? The shortest and longest. Thank you so much for your videos.
Thanks so much for watching the videos and sharing! Shortest time to PhD was 3 years (the minimum necessary, student had a MS already) and longest was 6 or 7 years. The average is 4.5 years. There's a list of my graduated PhD students in my CV www.dept.aoe.vt.edu/~sdross/Ross_CV.pdf
@@ProfessorRoss Thank you!
Sounds like a gyroscope pt. Special.