Graduate Yet another cross-product integral

  • Thread starter Thread starter Johan_S
  • Start date Start date
  • Tags Tags
    Integral
Click For Summary
The discussion revolves around the integration of a cross product and the validity of a specific integral expression involving vectors. The user questions the correctness of their integral formulation, expressing concern about potential sign issues. There is a request for clarification on the nature of the vector involved, specifically regarding the notation used for the integral. Additionally, a participant suggests that the expression might be misinterpreted as an inner product instead of a cross product. The conversation highlights the complexities of vector calculus and the importance of precise notation in mathematical expressions.
Johan_S
Messages
1
Reaction score
0
TL;DR
I am trying to figure out how to do a more complex cross-product integral and get stuck, and since my books are 1000 km away I turn to here
I am trying to integrate a cross product and I wonder if the following is true. It does not feel like it is true but it would be very nice if it was since otherwise I have a problem with the signs...

This is my first time posting here, so I just pasted in the LaTeX code and hope that it is parsed...

##\int\overline{r} \times \frac{d\overline{p}}{dt} \; d\overline{\phi} = - \int\overline{r} \times \frac{d\overline{\phi}}{dt} \; d\overline{p}##
 
Last edited by a moderator:
Physics news on Phys.org
What kind of vector ##\bar{\phi}## is ?

I observe two vectors in your integral
\int \mathbf{A} d\mathbf{B}.
Do you mean inner product
\int \mathbf{A} \cdot d\mathbf{B} ?
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
View full post »

Similar threads

Graduate Summing over continuum and uncountable numerocities
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Energy-to-angular momentum ratio in EM v. gravity quadrupole radiation
  • · Replies 0 ·
Replies
0
Views
1K
Undergrad Do Isometries Preserve Covariant Derivatives?
  • · Replies 14 ·
Replies
14
Views
4K
Integrals over chained functions
  • · Replies 1 ·
Replies
1
Views
2K
What Makes Differential Forms Click?
  • · Replies 12 ·
Replies
12
Views
4K
Undergrad Derivation of Crooks's Fluctuation Theorem
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Multiplying divergent integrals using Hardy fields approach
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Some notes on stochastic physics
  • · Replies 1 ·
Replies
1
Views
2K
MHB [ASK] Integral - Draining a Pipe
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Gaussian integral by differentiating under the integral sign
  • · Replies 19 ·
Replies
19
Views
4K