color(blue)"The equations of motion"The equations of motion are continuous function used to describe objects in movement under the action of one or more forces at constant acceleration affected by the environment too.
Examples:
=>⇒The momentum balance in the x and y directions are:
"∂u/∂t" + "u ⋅ ∇u" − f v = − ∂u/∂t+u ⋅ ∇u−fv=−"∂ϕ/∂x"∂ϕ/∂x − ∂/∂ z ( u ′ w ′ − ν ∂u/∂z ) + F_u + D_u
"∂v/∂t" + "v ⋅ ∇v" − f u = − "∂ϕ/∂x" − ∂/∂ z ( v ′ w ′ − ν ∂v/∂z ) + F_v + D_v
=>The time evolution of a scalar concentration field,
C ( x , y , z , t )
=>The equation of state is given by: ρ = ρ ( T , S , P )
=>The continuity equation for an incompressible fluid:
"∂u/ ∂x" + "∂v/∂y" + "∂w/∂z" = 0
=> Any motion equation can be established when a dependent variable will be changing with time, force, space, thermodynamics, or why not gravity fluctuation. Empirical correlations can be established or using the typical motion equations from literature.
