- #36
Studiot
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So where in this empty infinite universe is the origin of this reference frame?
...you define a reference frame.
Huh? What would make you think that? There are an infinite number of reference frames you can define.Studiot said:But I didn't, becuse there isn't one, or alternatively one can't.
It would change the momentum and any other frame variant quantities. It would not change any frame invariant quantities.Studiot said:If we let the velocity of the particle be v or 1010v, what difference would it make to this universe (or the particle)?
What is your thesis. State it clearly. You are not arguing a point right now, you are just bickering about stuff. That is not a way to have a conversation.Studiot said:I mentioned the word "force" precisely once in this thread, and that was before I asked a fluid mechanics related question.
Classical Mechanics is non-Relativistic. There is an absolute velocity. Fact that you aren't specifying velocity just means that you don't know its velocity, because you are being intentionally shifty about posing the question.Studiot said:In my opinion momentum in my uniparticular universe is indeterminate since the particle's velocity is indeterminate.
K^2 said:Lagrangian and Hamiltonian Mechanics are topics in Classical Mechanics. I'm not sure what your complaint is.
You are trying to artificially limit discussion to a static case. First of all, yes, any structural mechanics problem can be solved using Lagrange Multipliers without talking about forces. Of course, what you are actually analyzing is stress, so you have no choice but to involve forces at some point, and you might as well start balancing forces from the beginning.
Dynamics problems, however, are greatly simplified by use of Lagrangian and Hamiltonian Mechanics in generalized coordinates. That's kind of why you usually learn them in a Classical Mechanics course.
But hey, if you want Lagrangian analysis of a mass supported by the floor, here it is.
Lagrangian and constraint.
[tex]L = \frac{1}{2}m\dot{y}^2 - mgy + \lambda f(y)[/tex]
For a mechanical system, Lagrangian is equal to total kinetic energy of the system minus the total potential energy of the system. Later gives you the mgy term. There is also a term that goes with lambda. That's due to the constraint.Hetware said:How did you get mgy?
Isn't it simpler to just write down mass times acceleration, and be done with it?
The concept of force in mechanics refers to the physical quantity that causes an object to accelerate or change its state of motion. It is a fundamental concept in physics and is defined as the product of an object's mass and its acceleration.
Conservation laws, such as the law of conservation of energy and the law of conservation of momentum, play a crucial role in the concept of force in mechanics. These laws state that the total amount of energy and momentum in a closed system remains constant, meaning that forces acting on the system must balance out.
The primacy of conservation laws refers to the idea that these laws should be the starting point for understanding the concept of force in mechanics. Instead of focusing solely on the forces acting on an object, this approach emphasizes the conservation of energy and momentum in a system.
By prioritizing the conservation of energy and momentum, the concept of force in mechanics shifts from being a direct cause of motion to being a result of interactions within a system. This allows for a more holistic understanding of the physical world and can lead to new insights and discoveries.
Rethinking the concept of force in mechanics has significant implications for the study and application of physics. It challenges traditional ways of thinking and opens up new avenues for research and innovation. It also highlights the interconnectedness of physical systems and the importance of considering conservation laws in understanding the behavior of objects.