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AlephClo
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How to derive Nielsen equation from Lagrange equation
It was the first one I found too. But: Not good enough then, ... (*)AlephClo said:The best that I found is this
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.
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.
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.
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.
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.