I am a layman in aerodynamics. However, this is my view on your concern. In thermodynamics, $$dH=TdS+VdP$$ So, in an adiabatic, isobaric reversible process, ##dS=0, dP=0## the enthalpy##(H)## remains conserved.
Air is normally considered as insulator of heat. So if you consider a chunk of air...
OK, I understand the point. But at the same time I become a bit curious that you mentioned 'classical laws of physics are valid both forwards and backwards'. Does it imply quantum laws or more specifically Quantum mechanics lacks this symmetry?
That means to check the validity of time reversal symmetry, the prescription is to allow the system to evolve for a certain time (t, say), then flip the momentum of all particles and check that after the same time has been elapsed we get back the original state what we started with. Is it correct?
The state returns to the original only in case of periodic motion, I guess. A particle acted upon by a constant force will never come to its 'original'. Does it mean there is no time-reversal symmetry for such case?
It is said that Newton's laws of motion or laws of Quantum Mechanics posses time reversal symmetry but the second law of Thermodynamics does not. What I understand by the first part of the sentence is the following.
The dynamical state of a system changes with the increase of time. The state at...
The coordinate basis vectors defined as ##{\hat a}_q=\frac{\partial{\vec r}}{\partial q}## can indeed have a dimension. If I make a simple step out from Cartesian to Plane Polar coordinate system, then the coordinate basis vectors are
##{\hat a}_r={\hat r}##, ##{\hat a}_\theta={r\hat \theta}##...
Yes, you are right. It is unit matrix. But I meant to say something else. I found in wikipedia that the very name 'covariant' and 'contravariant' has been given purposefully according to their behaviour under basis transformation. Here is the link...
In some sources I found the reason behind this co-contra nomenclature is the way they transform under a basis transformation. I found the examples of contravariant vectors as position vector, velocity, acceleration etc. and that of covariant ones as grad(f). For contravariant vectors (or more...
Oh ok. I missed the 2nd page. This is the first time I get a fully satisfactory and clear answer. Another thing I want to make clear. As I understand the coordinate basis vectors are covariant basis vectors and the reciprocal basis vectors are contravariant. So a vector can be represented...
I don't know whether my question is write or not. Is there any way to obtain the covariant component of the same vector $$\vec{V}$$?
or is it just the components when written in terms of spherical coordinate unit vectors?