Equation of motion/ static equilibrium

[sara_87]

Homework Statement

I have notes on mechanics, and under the titile equation of motion/ static equilibrium there is the equation:

$$\rho$$$$\frac{\partial^2(u_i)}{\partial(t)^2}$$-$$\frac{\partial(\sigma_{ij})}{\partial(x_j)}$$=f_i(x,t)

Homework Equations

The Attempt at a Solution

I know that rho is the density, t is time, sigma is stress but what does the 'u' and 'f' represent?

thank you

 

[Jhero]

for your question! The 'u' in the equation represents the displacement vector and the 'f' represents the external force vector. The equation you have written is known as the equation of motion or Newton's second law of motion, which states that the net force acting on an object is equal to its mass times its acceleration. In this case, the left side of the equation represents the inertial forces (mass times acceleration) and the right side represents the external forces. This equation is often used to analyze the motion of objects in static equilibrium or undergoing uniform motion. I hope this helps clarify the meaning of the variables in the equation for you. If you have any further questions, please don't hesitate to ask!