Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
Intro Physics Homework Help
Advanced Physics Homework Help
Precalculus Homework Help
Calculus Homework Help
Bio/Chem Homework Help
Engineering Homework Help
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Homework Help
Advanced Physics Homework Help
Why is the Lie Bracket the same as the Cross Product for a 2 Sphere in R3?
Reply to thread
Message
[QUOTE="nigelscott, post: 6257729, member: 389949"] [B]Homework Statement:[/B] Prove that for a 2 sphere in R R[SUP]3[/SUP] the Lie bracket is the same as to cross product. [B]Relevant Equations:[/B] Vector: X = (y,-x,0); Y = (0,z-y) [X,Y] = J[SUB]Y[/SUB]X - J[SUB]X[/SUB]Y where the J's are the Jacobean matrices. Prove that for a 2 sphere in R[SUP]3[/SUP] the Lie bracket is the same as the cross product using the vector: X = (y,-x,0); Y = (0,z-y) [X,Y] = J[SUB]Y[/SUB]X - J[SUB]X[/SUB]Y where the J's are the Jacobean matrices. I computed J[SUB]Y[/SUB]X - J[SUB]X[/SUB]Y to get (-z,0,x). I computed (y,-x,0) ^ (0,z,-y) and obtained (xy,y[SUP]2[/SUP],yz) = (z,0,x) using Wolfram but I can't figure out why the sign of the x-component is different. Any help would be appreciated. [/QUOTE]
Insert quotes…
Post reply
Forums
Homework Help
Advanced Physics Homework Help
Why is the Lie Bracket the same as the Cross Product for a 2 Sphere in R3?
Back
Top