What is badminton for? -Part 6/.

...
So let us examine this claim of the priority of maths, in describing the game of badminton.
In badminton ‘energy’ is expended, but what is ‘energy’? Within Newtonian physics (that was good enough to get man on the moon) the definition of ‘energy’ can be stated:

“1/. When a force, F, acts on a body of mass, m, for a distance, d, it is useful to say that work, W, has been done on the body.”
For our purposes F in the case of a game is the application of a racquet, by a player, upon m, the shuttlecock, for a distance d, that the shuttle flys when struck. Thus W has been done on the shuttle and feathers are ruffled.


“2/.The work, W, is assigned a value W=Fd.
3/. You can therefore show that the work as defined by W=Fd is exactly equal to ½ mv²4/. The expression ½ mv² is also given a name. It is called the kinetic energy of the body.
5/. The more work (Fd) you put into pushing a body, the more kinetic energy (½ mv² ) it gets.”
(Reference: ‘Einstein for Beginners‘)

So the name of the game is for the ’Agent’ (player) ‘A’ to get a good whack of ½ mv² on the shuttlecock, within terms as described above.
But what of ‘A’ ? Also how do we describe mathematically the reality of an agent, acting within the bounded context of a game of doubles, so as to transform the mere whacking to a focus of three dimensional intent?
Each player can be considered as an ‘agent’ (A) within the following formulation;

Ee =(Aå Í ) + (Y J K L )