# Landau Classical Mechanics - Disintegration of particles

I am reading Landau's Classical Mechanics book and I'm having trouble understanding the concept of "internal energy". In Landau's words: the energy of a mechanical system which is at rest as a whole is usually called its internal energy.

He then considers a particle which spontaneously disintegrates (there are no external forces, so this system is closed) into two particles, which will be labeled 1 and 2. If we're in the frame K in which the initial particle is at rest, then by conservation of momentum we have that the two particles will move away from each other with momentums which are equal in modulus (let's call it $$p_0$$). Also, he says that conservation of energy implies $$$$E_i = E_{i1} + \frac{p_0^2}{2m_1} + E_{i2} + \frac{p_0^2}{2m_2}$$$$ where $$E_i, E_{i1}, E_{i2}$$ are the internal energies of the initial particle, particle 1 and particle 2 respectively. This is where I get lost because Landau has only explained (at least up to this point) how to write the Lagrangian of a closed system, but a single particle is not a closed system, since it could be interacting with the other particle. And if the two particles weren't interacting we would have $$E_{i1} = E_{i2} = 0$$, so what is the point of the formula above? Also, what is the expression for $$E_{ik}, \; k = 1, 2$$?

Am I missing something?

• Ok so, if I understood your argument, I have two make two assumptions, namely 1) that the particles 1 and 2 are actually composite bodies and therefore carry about "their own" potential energies $U_1$ and $U_2$ and 2) that I observe the two particles when any possible interaction between them is negligible (assuming thus that this interaction goes to zero when the distance between the two particles goes to infinity). Am I correct? Commented Apr 15, 2020 at 22:38