#color(blue)"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 = − ##"∂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.
