Using the Hamiltonian Method for Constrained Motion on a Cylinder Surface

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In summary, motion with constrain help is a type of motion where an object's movement is restricted or guided by external forces or constraints. It differs from regular motion in that the object's movement is limited and controlled. Examples of this type of motion include a pendulum swinging, a car driving on a circular track, and a person on a swing set. In science, motion with constrain help is used to study the effects of forces and constraints on an object's movement, and in everyday life, it has practical applications in machinery, sports, and transportation.
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scoroquantum
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motion with constrain help!

how do i use the hamiltonian method to find the equation of motion of a particle of mass h constrained to move on the surface of a cylinder defined by G2+t2=u2, where u is a constant. and the particle is subject to a force directed towards the origin and proportional to the distance of the particle from the origin: F=-kr.
 
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So, what have you tried?
 

1. What is motion with constrain help?

Motion with constrain help is a type of motion in which an object's movement is restricted or guided by some external force or constraint. This can include forces such as gravity, friction, or tension in a string.

2. How is motion with constrain help different from regular motion?

In regular motion, an object can move freely without any external forces or constraints. However, in motion with constrain help, the object's movement is limited or controlled by some external force or constraint.

3. What are some examples of motion with constrain help?

Examples of motion with constrain help include a pendulum swinging back and forth due to gravity, a car driving on a circular track, or a person swinging on a swing set.

4. How is motion with constrain help used in science?

Motion with constrain help is used in science to study and understand the effects of different forces and constraints on an object's movement. It is also used in experiments and simulations to model real-world scenarios and phenomena.

5. What are some applications of motion with constrain help in everyday life?

Motion with constrain help has many practical applications in everyday life, such as in machinery and technology, sports and recreation, and transportation. For example, pulleys and gears use motion with constrain help to transfer and amplify forces, while roller coasters and amusement park rides use it to create thrilling and controlled movements.

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