What is the meaning of gradient WRT a fixed point?

[teroenza]

My textbook (Taylor, Classical Mechanics) and professor introduced the concept of $\nabla$$_{1}$

to mean "the gradient of the function (potential energy) with respect to the position (x$_{1}$,y$_{1}$,z$_{1}$) of particle 1.

I do not understand this. I am familiar with partial derivatives and gradients with respect to general x,y,and z, but not with respect to a fixed point. I could not find anything from my calculus book to help.

 

[lugita15]

It's not gradient with respect to a fixed point. It's just that the potential energy is a function of both the position of particle 1 and the position of particle 2, so you could write V(x1,y1,z1,x2,y2,z2). When he says gradient with respect to the position of particle 1, he means we should calculate partial derivatives with respect to x1, y1, and z1, not x2, y2, and z2.

 

[teroenza]

Ok so it would be just a regular gradient, but WRT particle 1 means I treat x2,y2,z2 as constants. Thanks

 

[lugita15]

Ok so it would be just a regular gradient, but WRT particle 1 means I treat x2,y2,z2 as constants. Thanks

Yes, exactly.