Dynamics Moments - Linear Algebra / Cross Product

[udtdewclaw]

Some background: I am self studying dynamics and I have encountered a fundamental problem with either my understanding of linear algebra, or I am just plain dumb. So, I print screened the page of the book we're on. Now let me try to reduce some ambiguity in my question, I have a general understanding of the cross product and unit vectors. With this question it's stating the G is the momentum of the particle is G = mvn, where n is the unit vector in the direction of velocity. When we try to take the moment of the position vector from O to P with the momentum we get, M(G/O)[G with respect to O] =p(P/O) ×G=p(Q/O) ×G

=y_0*n*y ×m*v*(cosθn_x +sinθn_z)

=m*v*y0(sinθn_x −cosθn_z). * indicated multiplication, obviously.

My question is, how does G = mvn, => G = mv(cosθn_x +sinθn_z) or more specifically, how does n = (cosθn_x +sinθn_z) and further deductions until the end result. And can someone explain intuitively what a 'moment' is? I would like a full explanation of these mathematical deductions if possible.

Here is a link to the book: Fundamentals of Applied Dynamics - Tenenbaum

http://f3.tiera.ru/2/P_Physics/PC_Classical%20physics/PCtm_Theoretical%20mechanics/Tenenbaum%20R.A.%20Fundamentals%20of%20applied%20dynamics%20%28Springer,%202004%29%28ISBN%20038700887X%29%28O%29%28730s%29_PCtm_.pdfHere is a screenshot of the page of the book also, Fundamentals of Applied dynamics - Tenenbaum - Page 33.

I also have a post on math.stackexchange asking the same question however, stack exchange has a latex version of the equations for easier reading, here is a link
http://math.stackexchange.com/questions/641029/cross-product-moments-dynamics

 

[voko]

I wonder why Tenenbaum had to introduce notation that nobody understands and that is different from mainstream texts on mechanics.

The result follows by using the properties of the vector (cross) product. Re-read Appendix A and make sure you do the exercises.

It is probably a little early to explain what "moment" is generically. It will confuse you even more. Just stick with the narrative of the book for now, it should give you more concrete examples of moments shortly.

 

[udtdewclaw]

I wonder why Tenenbaum had to introduce notation that nobody understands and that is different from mainstream texts on mechanics.

The result follows by using the properties of the vector (cross) product. Re-read Appendix A and make sure you do the exercises.

It is probably a little early to explain what "moment" is generically. It will confuse you even more. Just stick with the narrative of the book for now, it should give you more concrete examples of moments shortly.

Okay thanks, can you go to my stack exchange thread and tell me if I figured out my first question ( question A) correctly, I posted my solution to it at the bottom of the post.

 

[voko]

I suggest that you go to the Homework Help forum and start a thread there, and post your attempt at the solution there. That is how it works here, doing it the way you want is uncommon and may be against the rules here.

 

[udtdewclaw]

I suggest that you go to the Homework Help forum and start a thread there, and post your attempt at the solution there. That is how it works here, doing it the way you want is uncommon and may be against the rules here.

Okay thanks.