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AlephClo
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How to derive Nielsen equation from Lagrange equation
How to derive Nielsen equation from Lagrange equation?
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In summary, the conversation is about trying to derive the Nielsen equation from the Lagrange equation. The person has done research and found a possible solution, but is unsure about the origin of the commutator and the (2) relationship. They ask for clarification and BvU responds by suggesting another source to look into and explaining the meaning of the commutator.
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BvU
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Isn't google your friend ? What did you find so far ?
- #3
AlephClo
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I have done couple hours of research and tried to derive it myself. The best that I found is this, but I do not understand where the commutator come from. It does not seem to be the Poisson braket commutator applied to T either (A,B) = AB-BA . Nor that I understand where the (2) relationship comes from. Thank you
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BvU
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It was the first one I found too. But: Not good enough then, ... (*)AlephClo said:
What about the second one in the list I got ?
Except where it says ##=0## one should read ## = Q_j## (*) And yes, the commutator [A,B] means: first B then A minus first A then B.
- #5
AlephClo
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Thank you BvU.
Related to How to derive Nielsen equation from Lagrange equation?
1. What is the Nielsen equation?
The Nielsen equation is a mathematical formula that describes the motion of a particle in a conservative force field. It is derived from the Lagrange equation, which is a fundamental principle in classical mechanics.
2. What is the Lagrange equation?
The Lagrange equation is a mathematical equation that describes the motion of a system by taking into account the kinetic and potential energies of the system. It is based on the principle of least action and is widely used in classical mechanics and physics.
3. How is the Nielsen equation derived from the Lagrange equation?
The Nielsen equation is derived by applying the Lagrange equation to a specific form of the potential energy function, known as the Nielsen potential. This potential is based on a special type of force field called a central force field, and the resulting equation describes the motion of a particle in this type of force field.
4. What are the applications of the Nielsen equation?
The Nielsen equation is commonly used in classical mechanics to study the motion of particles in central force fields, such as those found in celestial mechanics. It is also used in other fields, such as astrophysics and plasma physics, to model the behavior of particles in various force fields.
5. Are there any limitations to the Nielsen equation?
Like any mathematical model, the Nielsen equation has its limitations. It is based on certain assumptions, such as the particle being in a central force field and the force field being conservative. It also does not take into account relativistic effects and is not applicable to systems with multiple particles. Therefore, it is important to carefully consider the context and applicability of the Nielsen equation when using it in scientific research.
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