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write the hamilton equation for point mass moving in a straight line?

write the hamilton equation for point mass moving in a straight line?

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Answer #1

As the particle is moving aling straight line, the motion of the particle is one dimentional. So I will take the position of the particle at time ' t ' as x = x(t).

You have not given any expression for the potential energy of the particle. So I will assume the potential is a function of x, and denote it by V(x).

If it a free particle in one dimension, then just put V(x) = 0.

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Let's take the mass of the particle is ' m ', the velocity of the particle is ' v ', the momentum of the particle is ' px ' .

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