Why is the momentum a covector? - Mathematics Stack Exchange
2015年6月14日 · In the general case (real case!) on configuration manifold at a specific point $(q,\dot q)$, momentum is not a vector parallel to $\dot q$ at all. Rather it is a question: if I'd …
How to calculate the derivative of the angular momentum vector
2020年12月25日 · The parallel component of the velocity vector $\vec v_{{}={}}$ is not part of the angular momentum vector. The perpendicular component of the velocity vector can be …
How can angular velocity or angular momentum be a vector?
Similarly, angular momentum is the derivative of kinetic energy with respect to angular velocity, so it is a gradient, which is a (dual) vector (to angular velocity). There's an interesting mapping …
What does the cross product of the velocity and position vector …
2021年2月21日 · Physically, the cross product of momentum and velocity is the angular momentum $\mathbf{L}=\mathbf{r}\times\mathbf{p}$, which is what we're talking about here if …
Elastic Collision Between Equal Masses in Vector Form
2020年9月1日 · I am looking for a derivation of these vector formulas for final velocities, starting from convervation of momentum and energy assumption. I've seen a lot of literature on them …
differential geometry - How is the generalised momentum a …
2018年4月30日 · Note that the coordinates of a co-vector are covariant, while the coordinates of a vector are contravariant. $\endgroup$ – Lutz Lehmann Commented May 1, 2018 at 13:26
Calculating the angular momentum of a rotating sphere
2022年1月13日 · You also know that since this is a sphere, the angular momentum will be parallel to the axis of rotation. You find the magnitude of the angular momentum to be $\frac25MR^2.$ …
What do physicists mean when they say something is "not a vector"?
2023年12月19日 · Like (0,0,1) is only a vector if it changes appropriately in each coordinate system (so it can stay fixed in your space). Or more instructive: angular momentum, almost …
mathematical physics - Poisson brackets of angular momentum ...
2016年6月2日 · $\begingroup$ @TomD1 Well, each of the four terms obtained upon distribution ends up yielding exactly one nonzero bracket, so things simplify more than you might realize.
Hermitian adjoint for 3-vectors; should the energy-momentum 4 …
2024年1月4日 · Consider the real Klein-Gordon scalar; Taking the Hermitian Hamiltonian, and (spatial) momentum operators as $$\\hat H = \\int \\frac{d^3 \\vec p}{\\left(2 \\pi ...