I'm quite curious as to whether there is an equation (whether it be in scalar, vector, or tensor form) that defines the acceleration of a particle as a function of the three space coordinates and time. My curiosity arose when I was thinking of the one dimensional equation: a = v*(dv/dx); where the acceleration and velocity are only defined in the x-direction. I thought the generalization to three dimensions would be: a = vx*(dvx/dx)i + vy*(dvy/dy)j + vz*(dvz/dz)k To include the time variable I thought it might just be the material derivative of acceleration (like in fluid mechanics). These assumptions are just based on my gut feeling (I have done no derivation whatsoever). Is there an actual equation?