
Classical state of a particle lives in the 2n-dimensional manifold known as phase space. The coordinates of the phase space are the configuration space and the corresponding conjugate momenta. The state is a single point on the phase space, corresponding to the initial conditions of the problem. The Hamiltonian determines the time evolution in the phase space, which is a trajectory.
To make is simpler for you to understand: 1. Position and momentum couples form the physical state. And of course, for any physical system, it exists. 2. You need 2 initial conditions to solve a 2nd order differential equation. You can't solve a differential equation without initial conditions (of course to use this fact, you would need to understand that F=ma is a differential equation, not a function) (Maybe it's better if you read some good introductory text, such as Feynman Lectures on Physics Vol 1, Chapter 9).
If still not clear for you: the initial state in a two body problem is determined by the initial position and velocity. They are the initial conditions of your "function" F=ma, which is actually a second order differential equation. F determines how this initial state will change over time.
If at some point you found Physics wonderful, and then lost it when everything became calculations, I wholeheartedly recommend this book, and the other volumes once you are done with it.
Feynman has an engaging conversation style, and when you are immersed in the book, you literally feel the wonders of the universe. You go through Newton's motion and gravitation laws, and then using simple numerical methods, he plots you the orbital path around the sun of a given planet.
It does has derivations, but it doesn't let derivation take over the idea it's discussing. And some derivations and deductions will be enlightening when you already know something about something - for e.g for the first time in my life, I saw why the observed velocity won't exceed speed of light.
Even for the ideas I know, Feynman's explanation either add something, or make me thing "Holy Shit I didn't think of it that way." While discussing Newton's laws, he mentions this whole set of laws depends on a coordinate system - but we really can't say all experiments are to be performed at place x - but you know what, these laws are independent of the axis you choose, and here is how.
You are left thinking, hell, I kinda knew it but didn't approach it that way.
Then he will tell you a system moving with constant velocity in a straight line will observe the exact same laws of physics, and here is why, which is just an extension of the previous axis transform.
Even if you don't like Physics, give this book a try. Most likely you will understand universe better when you are through.
>“If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.” ― Richard Feynman, The Feynman Lectures on Physics Vol 1
This should be generalized and augmented to the idea of analysis and synthesis in general, what we could call "general alchemy". That is physical and symbolic isolation & scientific controls help to understand the world, but we also need to figure out the "chemistry" so to speak of how things tend to combine and transform so we can understand the whole ecology of the integrated system.
The freedom to choose among terabytes would take a ton of thought to actually come up with some optimal set. You could probably churn over thoughts on the subject for years.