Search Results

Consider as space coordinates $q_1,q_2,q_3$ why if the metric tensor is not constant in space $q_1, q_2, q_3$ can't be considered a displacement vector? And why vice versa, a constant metric tensor in …

I'm studying Minkowski space time (M4) and they say it's a 4 dimensions real affine space. M4 is an affine space so there is a non-empty set A, a 4 dimension real vector space V, and there is a functi …

Let's use the spherical coordinates so that $\vec P=(r, \theta, \phi)$. In this context i've read that it's possible to write $$\vec P'=\vec P + d\theta\ \vec e_\theta+d\phi\ \vec e_\phi+dr\ \vec e_r$ …

I was thinking about how to use different coordinate systems in 3D space and how to describe curved surfaces embedded in 3D space when I realized that all the notations I know make sense only if every …

Landau vol.2 first chapter explain special relativity, and in particular it is considered the case of two frame of references $K$ and $K’$ such that the axis $x$ and $x’$ are coincident while $y$ and …

I've seen many times the angular momentum operators $\hat L_x, \hat L_y,\hat L_z$ expressed in spherical coordinates but I've never seen the components operators $\hat L_\rho, \hat L_\theta, \hat L_\p …

Imagine an ant on a sphere that perceives only two dimensions. Is there a coordinate system that allows the ant to describe the position with the position vector?

I'm studying about curved spaces and I read that a manifold is flat if there a coordinate system such that the metric tensor is constant everywhere. Then I also read that when the space-time tensor i …

I can find 3 displacement $\vec d_1 ,\vec d_2, \vec d_3$ and use them as basis so that a displacement is $\vec d=a\vec d_1 +b\vec d_2+c \vec d_3$. I can find 3 forces $\vec F_1 ,\vec F_2, \vec F_3$ an …

This question could sound silly but I though a lot about it and I'm not new to physics. Let's say I have a plane on which I use polar coordinates, it means a point $P$ can be indicated by its coordin …

Some active transformations on the system can be seen also as passive transformations, for example the rotation of the system can be seen as the rotation of the observer in the opposite direction. Any …