MHB Multivariable conservative field

kenporock
Messages
3
Reaction score
0
Goodnight,

How can I find a conservative field F, such that ∫F ds = 0 without C being a closed path
Can i have some examples ?
 
Physics news on Phys.org
kenporock said:
Goodnight,

How can I find a conservative field F, such that ∫F ds = 0 without C being a closed path
Can i have some examples ?

Hi kenporock, welcome to MHB! (Wave)

Consider the force of gravity.
Now move an object around, such that it ends up on the same height it had at the beginning.
The work done by gravity $∫\mathbf F\cdot d\mathbf s$ is then zero.
That is, the object has the same potential energy again.
 
For original Zeta function, ζ(s)=1+1/2^s+1/3^s+1/4^s+... =1+e^(-slog2)+e^(-slog3)+e^(-slog4)+... , Re(s)>1 Riemann extended the Zeta function to the region where s≠1 using analytical extension. New Zeta function is in the form of contour integration, which appears simple but is actually more inconvenient to analyze than the original Zeta function. The original Zeta function already contains all the information about the distribution of prime numbers. So we only handle with original Zeta...
Back
Top