Newtons second law on positive real line R+

In this work, a classical particle that moves on ℝ+ will be investigated by using the affine commutator relation which corresponds to the Poisson bracket in classical mechanics where the equation of motions and the Newton’s second law will be modified. Two example of physical systems will be studied further using the modified Newton’s second law namely free particle and harmonic oscillator. The result concludes that for a free particle, the force on ℝ+ is no longer zero and a linear force due positive real line and fixed momentum. While, classical dynamics on ℝ+ for simple harmonic oscillator system is a qubic force.

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