NP 2 - Review of classical mechanics used in following...

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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei Review of classical mechanics used in following pages g ,..., 2 , 1 i ), t , q ( U ) t , q , q ( K L i i i = = K – kinetic energy, U – potential energy, q i – coordinates, – velocities, g - number of degrees of freedom Equations of motion: 0 q L q L dt d i i = Integral of motion: const L q L q i i i = = + = + = i i i i i i i i i i i i i i i q q L dt d q q L q L dt d q q q L q q L dt dL ) x ,..., U(x 2 x m L 3N i i 2 i = Lagrangian of a classical N-body system: Equations of motion: Integral of motion: ) x ,... x ( U x x m N 3 1 i i = E ) x ,..., U(x 2 x m 3N i i 2 i = + & 0 t L = Lagrangian: i q &
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University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei PV ) d V ,..., d V ( U . E . P N 3 3 / 1 1 3 / 1 + = 2 V M 2 d mV . E . K 2 i 2 i 3 / 2 + =
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This note was uploaded on 02/14/2012 for the course MSE 4270 taught by Professor Zhigilei during the Fall '11 term at UVA.

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NP 2 - Review of classical mechanics used in following...

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