The software solves
equations of motion for every frame of an effect, as it understands the physics of how things are supposed to move and behave.
A general circulation model (also known as a global climate model, both labels are abbreviated as GCM) uses the
same equations of motion as a numerical weather prediction (NWP) model, but the purpose is to numerically simulate changes in climate as a result of slow changes in some boundary conditions (such as the solar constant) or physical parameters (such as the greenhouse gas concentration).
Almost 20 years later, Jean Le Rond d'Alembert followed a similar procedure, but he focused on simplifying
the equations of motion rather than their solutions.
He used Newton's laws to write down the system's
equations of motion, and solved them.
He sat in his office and scrutinized 30 published attempts at writing
the equations of motion for a bicycle.
The principle of the first method lies on the numerical solution of Newton's
equations of motion to propagate the system, whereas the second stochastically generates states of a system according to a predetermined statistical mechanical probability distribution.
There are some references to formula such as the Cosine Rule and
an equation of motion.
My point is that the choice of origin relative to which to describe
the equations of motion is arbitrary — and transformation between them readily possible — , but some choices are «nicer» than others.
The hydrostatic equation is the vertical component of the momentum equation (Newton's
equation of motion) for the fluid parcel when the forces are in perfect balance and the net acceleration = 0.»
However,
the equations of motion are based on the assumption that they only be applied in the troposphere.
Global models of the tide height and depth - averaged tidal currents are based on the well - understood physics of gravitational forcing by the Moon and the Sun, and
the equations of motion for the ocean.
«You could stare at
the equations of motion all day and you will not see this possibility.
The time scale of variability of the patterns is longer than the decorrelation time scale of the stochastic forcing, because of the temporal integration of the forcing by
the equations of motion limited by the effects of nonlinear dynamics and friction.