The Difference Between Newtonian Mechanics, Lagrangian Mechanics and
Hamiltonians in Solving Problems About Motion
An object with mass m is released on an incline without force, so it slides down. Assume that the
inclined plane has no coefficient of friction (slippery plane). Determine the equations of motion
according to Newtonian mechanics, Lagrangian mechanics and Himiltonian!
Answer:
1. Newtonian Mechanics
Newtonian mechanics is a physical phenomenon that is solved using Newton's laws. This
means that every problem regarding motion is always viewed from a force acting on an
object. So to determine the equation of motion in the above problem we must use Newton's II
law:
d2 x
Where : ∑ F=m , so the equation is
dt 2
d2 x
mg sin θ=¿ m ¿
dt 2
2
d x
−g sin θ=0
dt 2
Hamiltonians in Solving Problems About Motion
An object with mass m is released on an incline without force, so it slides down. Assume that the
inclined plane has no coefficient of friction (slippery plane). Determine the equations of motion
according to Newtonian mechanics, Lagrangian mechanics and Himiltonian!
Answer:
1. Newtonian Mechanics
Newtonian mechanics is a physical phenomenon that is solved using Newton's laws. This
means that every problem regarding motion is always viewed from a force acting on an
object. So to determine the equation of motion in the above problem we must use Newton's II
law:
d2 x
Where : ∑ F=m , so the equation is
dt 2
d2 x
mg sin θ=¿ m ¿
dt 2
2
d x
−g sin θ=0
dt 2
