Energy of one mass in a Hamiltonian System

In summary, the conversation was about a person asking for help with their math thesis and checking their calculations for a simulation of a one dimensional chain of masses and linear springs. The system is Hamiltonian, meaning its total energy is constant, and the calculations showed that no energy was lost. The question was raised if the sum of one mass' kinetic and potential energy should also be constant.
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IamNoEinstein
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Hi. I hope this is in the right spot - I am not a physics major so not sure if it qualifies as classical, quantum, or other type of physics). I am asking the following to check the calculations of my graduate math thesis

I am simulating a one dimensional chain of masses and linear springs (that is, springs with Force=-kx). The system is Hamiltonian, so it's total energy is constant. My calculations show that the entire system does not lose any energy.

Should the sum of one mass' kinetic and potential energy also be constant?
 
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FAQ: Energy of one mass in a Hamiltonian System

What is the Hamiltonian system in physics?

The Hamiltonian system is a mathematical formalism used to describe the dynamics of a physical system. It is based on the Hamiltonian function, which represents the total energy of the system. This function takes into account the position and momentum of all particles in the system.

2. What is the role of energy in a Hamiltonian system?

Energy is a fundamental concept in a Hamiltonian system. The Hamiltonian function represents the total energy of the system, and it is used to calculate the equations of motion for all particles. The energy of one mass in a Hamiltonian system is the contribution of that particular mass to the overall energy of the system.

3. How is the energy of one mass calculated in a Hamiltonian system?

The energy of one mass in a Hamiltonian system is calculated by taking the dot product of its position and momentum vectors. This is represented by the Hamiltonian function, which is a function of both position and momentum variables. The resulting value is the energy of that mass in the system.

4. What is the significance of the energy of one mass in a Hamiltonian system?

The energy of one mass in a Hamiltonian system is significant because it represents the contribution of that mass to the overall energy of the system. This energy can be used to determine the motion of the mass and how it interacts with other particles in the system. It also plays a crucial role in understanding the behavior and stability of the system.

5. How does the energy of one mass affect the dynamics of a Hamiltonian system?

The energy of one mass in a Hamiltonian system affects the dynamics of the system by determining the trajectory and motion of that mass. It also influences the motion of other particles in the system through interactions and exchanges of energy. Changes in the energy of one mass can lead to changes in the overall energy and dynamics of the system.

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