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Unformatted text preview: x (1.10) (1.11) 3 Formally, the linear Eq. (1.1) and the linear, second order differential Eq. (1.2) have been
transformed into the two linear, first order partial differential Eqs. (1.10) and (1.11). Despite this
formal difference, the physical content of the newtonian and the hamiltonian formulation is
1.4 Breakdown of classical mechanics
One of the characteristics of classical mechanics is the continuous, non-discrete nature of its
variables position, x(t), and momentum, p(t). That is, a particle can have any (non-relativistic)
momentum with no restrictions imposed by the axioms of classical mechanics. A second
characteristic of classical mechanics is the deterministic nature of time dependent processes.
Once initial conditions of a mechanical problem are known (that is the position and momentum
of all particles of the system), the subsequent evolution of particle motion can be predetermined
according to the hamiltonian or newtonian equations of motion. In its final consequence,
determinism would predetermine the entire universe from its birth to...
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- Fall '12