Why is it important that Hamilton’s equations have the four symplectic properties and what do they mean?

The symplectic properties are: time invariance conservation of energy the element of phase space volume is invariant to coordinate transformations the volume the phase space element is invariant with respect to time I’m most inerested in what 3 and 4 mean and why they are important. Answer Coordinate invariance guarantees that the phase space M … Read more

What are some interesting calculus of variation problems? [closed]

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for … Read more

Can relativistic kinetic energy be derived from Newtonian kinetic energy?

Relativistic kinetic energy is usually derived by assuming a scalar quantity is conserved in an elastic collision thought experiment, and deriving the expression for this quantity. To me, it looks bodged because it assumes this conserved quantitiy exists in the first place, whereas I’d like a derivation based upon using KE =12mv2 in one frame, … Read more

Why are non-horizontal levers not considered to be in equilibrium?

Consider a triple-beam balance, like so: (source: microscopesamerica.com) An unknown mass is placed on the left pan, and the provided weights are moved on the right until the lever arm comes to rest at an exactly horizontal position, as indicated by a line on the rightmost tip of the lever arm. Often, when I’m using … Read more

Could two identical stars revolve around each other in a common orbit if we only account for Newtonian physics?

Both a parent star and its planet revolve around the center of mass of the system, the reason we see stellar wobble. But if we take this to be true, which it is, there can be a configuration in which two identical stars revolve around their center of mass, in a common orbit. What I … Read more

Phase space Lagrangian?

Reading out of this lecture series we define a phase space Lagrangian L to be a function of 4n+1 variables namely q,˙q,p,˙p,t. My question is, what space is this function defined on? (I know that the ˙p is there for names sake only). My stab at an answer is it is a product space between … Read more

What is the time period of an oscillator with varying spring constant?

It is well known that the time period of a harmonic oscillator when mass m and spring constant k are constant is T=2π√m/k. However, I would be interested to know what the time period is if k is not constant. I have searched hours after hours for right answers from Google and came up with … Read more

When to use Quantum Mech.? [closed]

Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 6 years ago. Improve this question Is there any parameter (in terms of physical quantities such as mass, length, charge…) which … Read more

What is the rigorous quantitative definition of the concept of “Energy”? [closed]

Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 5 years ago. Improve this question First of all I acknowledge you that I posted this Question on many other forums and Q&A Websites. So don’t … Read more