Momentum, or, Why I will always beat you

At the risk of causing injury to you, I will now introduce some physics. If you find yourself unable to lift the required weight; resign yourself to a life of tedium and serfdom, for the free and great life of a barbarian is far beyond your abilities.

Every barbarian must have an acute understanding of physics, be it while fighting in glorious hand to hand combat, sailing your longship to ripe pillaging fields or calculating the trajectory a system undergoes through state space during a scattering process whilst remaining Lorentz -covariant.

Without being marred with philosophy, I shall make a few statements which are self evident (AGAIN, LOGIC!) and then construct the foundations of what may be called "Newtonian Mechanics", after one of the great barbarians: Newton the Madaxe (although most sources erroneously call him Isaac Newton)

Space can be considered as an ordered collection of numbers $(x,y,z)$ such that $x,y,z \in \mathbb{R}$. Upon fixing the 3 numbers representing some specific location in space, such as yourself, all other points may be unambiguously defined.

A simple way to do this systematically is to decide on a left and right, forward and back, up and down while the numbers $x,y$ and $z$ would correspond to a distance from the initial fixed point along those directions.

We can now know where everything is! However, bitter experience has shown us that things do not necessarily remain where they are right now. So therefore, we require a measure of time, $t \in \mathbb{R}$.

We also require another quantity mass, $m \in \mathbb{R}$, which encompasses "how much" of something there is.

From these we can extract the necessary physics.

An object of mass $m$ can therefore be labelled by a succession of different positions $(x,y,z)$ for every time $t$, with time constantly increasing.

Define the velocity $\bold{v} = (\dot{x}, \dot{y}, \dot{z})$ of an object by the change of positions divided by the change in times, as the change in time goes smaller and smaller.

In other words:

$\dot{x} = \frac{x_1 - x_2}{t_1 - t_2}$ where $x_1$ is the value of $x$ at time $t_1$, and so on, while $t_1$ is 'almost' equal to $t_2$

$\dot{y}, \dot{z}$ are defined in a similar way.

A quantity of particular importance in physics is momentum. It is defined as
$m\bold{v} = (m \times x, m \times y, m\times z)$. From now on, for convenience, the symbol $\times$ will be omitted. You should know enough by now when we mean multiplication because of the context! If not, don't worry. Not everyone can be a barbarian, someone has to be pillaged!

The great discovery of early barbarians was that if you have another body, and it hits another body, if you add the two momentums before and after the collision, it does not change.

Already, you can see the applications such a discovery has on axe fighting!

Keep at it, wimps!