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Gregg
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I have found that ##J = m r^2 \sin^2 \theta \dot{\phi}^2 ## is a constant of motion. How is this orbital angular momentum in the ##\theta = 0 ## direction? It is a particle moving in a central force field.
Gregg said:I have found that ##J = m r^2 \sin^2 \theta \dot{\phi}^2 ## is a constant of motion. How is this orbital angular momentum in the ##\theta = 0 ## direction?
A constant of motion is a quantity that remains unchanged over time in a physical system. It is a fundamental concept in classical mechanics and is used to describe the behavior of systems such as particles, fluids, and gases.
The concept of constant of motion is important because it helps us understand and predict the behavior of physical systems. It allows us to identify quantities that will remain unchanged, even as other variables may change. This helps us make accurate predictions and analyze the dynamics of systems.
Examples of constants of motion include energy, momentum, angular momentum, and electric charge. In classical mechanics, these quantities remain constant as long as the system is isolated and not acted upon by external forces.
Constants of motion are closely related to symmetries in physical systems. In fact, Noether's theorem states that for every continuous symmetry in a system, there is a corresponding constant of motion. This connection between symmetries and constants of motion is a fundamental principle in physics.
In classical mechanics, a constant of motion remains unchanged as long as the system is isolated and not acted upon by external forces. However, in some systems, such as quantum systems, constants of motion may change due to quantum effects. In general, a constant of motion can change if there is a violation of the conditions that keep it constant.