Register to reply

Integral with dot products

by nos
Tags: integral, products
Share this thread:
nos
#1
Nov20-12, 03:45 AM
P: 32
Hi everyone,

I'm trying to understand the integral on http://www.phys.lsu.edu/~jarrell/COU...p14/chap14.pdf (page 14)

I get all the steps except the how to get from eq. 48 to eq 49. I'm not really sure how to compute all the dot products. He lets the angle between n and β be θ
and angle between β and [itex]\dot{β}[/itex] be θ(0)

Attempt at solution:

[itex]n\cdotβ=βcos(θ)[/itex]
[itex]β\cdot\dot{β}=β\dot{β}cos(θ(0))[/itex]
[itex]n\cdot\dot{β}=\dot{β}cos(θ-θ(0))[/itex]?

If this is correct, do I proceed by applying the difference identity of cosine in the last dot product and then square the whole thing? There are going to be a lot of terms, so before wasting more time on expanding, let's first see if what i'm doing is in fact the right way to do this integral.

Many thanks!
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history
haruspex
#2
Nov21-12, 12:42 AM
Homework
Sci Advisor
HW Helper
Thanks
P: 9,657
Quote Quote by nos View Post
[itex]n\cdotβ=βcos(θ)[/itex]
[itex]β\cdot\dot{β}=β\dot{β}cos(θ(0))[/itex]
[itex]n\cdot\dot{β}=\dot{β}cos(θ-θ(0))[/itex]?
You could only do something like that if you know the three vectors are coplanar. Are they?
nos
#3
Nov21-12, 01:31 AM
P: 32
Yes that is whats been troubling me. I am not sure. But how else do you go from eq 48 to eq 49?

haruspex
#4
Nov21-12, 03:00 AM
Homework
Sci Advisor
HW Helper
Thanks
P: 9,657
Integral with dot products

Sorry, I can't follow it either. I strongly suspect a typo, like a β that should be a β-dot or vv., but I haven't been able to find a simple explanation.
nos
#5
Nov21-12, 03:07 AM
P: 32
Oh well, thanks very much anyway for replying:)


Register to reply

Related Discussions
Cross products vs. dot products Introductory Physics Homework 2
Matrix - Inner Products and Dot Products Calculus & Beyond Homework 3
Integral of products? Calculus & Beyond Homework 2
Integral Domains: Products of Irreducibles Calculus & Beyond Homework 2
Questions concerning cross products, dot products, and polar coordinates Introductory Physics Homework 1