How Many Additive Integrals of Motion Exist in a Closed Mechanical System?

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In summary, The question asks how many additive integrals of motion exist for a closed mechanical system described by s generalized coordinates. The answer is 7, as there are 2s-1 independent integrals for this system, including energy, momentum, and angular momentum.
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S.P.P
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Hi all,

Was given a question which went like this:

Consider a closed mechanical system described by s generalized coordinates qi. How many additive integrals of motions exist for this system?

I'm not quite sure exactly what is meant by this. I know that there are 2s-1 integrals for this closed system, but how do I go about finding out how many additive integrals there are. I also know that there are 7 additive integrals important to classical mechanics, energy, and the 3 components of momentum, and 3 of angular momentum. So is the answer just 7, or is there something I've missed?

Thanks for any help
 
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That should read:

'I know that there are 2s-1 independant integrals for this closed system'
 

Related to How Many Additive Integrals of Motion Exist in a Closed Mechanical System?

1. What is classical mechanics?

Classical mechanics is a branch of physics that deals with the motion of macroscopic objects, such as particles, systems of particles, and rigid bodies. It is based on Newton's laws of motion and the law of universal gravitation.

2. How does classical mechanics differ from quantum mechanics?

Classical mechanics describes the behavior of macroscopic objects, while quantum mechanics describes the behavior of microscopic particles. Classical mechanics is deterministic, meaning that the future state of a system can be predicted given its initial conditions, while quantum mechanics is probabilistic, meaning that the future state of a system can only be described in terms of probabilities.

3. What are the main principles of classical mechanics?

The main principles of classical mechanics are Newton's laws of motion, which state that an object will remain at rest or in motion at a constant velocity unless acted upon by an external force, and the law of universal gravitation, which describes the force of gravity between two objects.

4. What are some real-world applications of classical mechanics?

Classical mechanics has many practical applications, such as designing bridges, buildings, and other structures, developing vehicles and machines, predicting the motion of celestial bodies, and understanding the behavior of fluids and gases.

5. Can classical mechanics explain all physical phenomena?

No, classical mechanics cannot explain all physical phenomena. It breaks down when dealing with extremely small particles, high velocities, and strong gravitational fields. In these cases, quantum mechanics and relativity are needed to fully understand and describe the behavior of the system.

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