Conservation laws and Noether's theorem

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Classical Mechanics and Relativity: Lecture 8
Theoretical physicist Dr Andrew Mitchell presents an undergraduate lecture course on Classical Mechanics and Relativity at University College Dublin. This is a complete and self-contained course in which everything is derived from scratch.
In this lecture I discuss conservation laws within the Lagrangian formulation of classical mechanics. I show why certain physical quantities are conserved (do not change with time), and the conditions for which this arises. In the second part I introduce Noether's theorem, which makes the deep connection between continuous symmetries and conservation laws. We will see explicitly how translational invariance is responsible for conserved linear momentum, while rotational symmetry implies conservation of angular momentum.
Full lecture course playlist: • Classical Mechanics an...
Course textbooks:
"Classical Mechanics" by Goldstein, Safko, and Poole
"Classical Mechanics" by Morin
"Relativity" by Rindler

Пікірлер: 5

@miss8888m Жыл бұрын

I honestly wish I can give you more than one like, this was really helpful. Thank you very much for this well explained lesson.

@berkelium5534 Жыл бұрын

Thank you so much sir

@eamon_concannon 2 жыл бұрын

13:11 I've got this by calculating the z component of the angular momentum of the particle about the origin using standard basis vectors i.e. z-component of (r X dr/dt) = z-component of (xi+yj+zk) X (dx/dt i + dy/dt j + dz/dt k) = x dy/dt- y dx/dt and then changing to spherical coords. Also, this is the same as the z component of the angular momentum of the particle about the z-axis i.e. z-component of (xi+yj) X (dx/dt i + dy/dt j + dz/dt k) = x dy/dt- y dx/dt. Intuitively, if θ and r are constant, then the velocity of the particle using spherical basis vectors e_φ, e_r and e_θ is (rsinθ dφ/dt)e_φ and the result follows.