Answered: State and prove Liouville's Theorem.… | bartleby

Related questions

Question

State and prove Liouville's Theorem.
(q.p+dp)
B
р
0
q
speed
i. e.
df
dt
A
(q.p)
N
-
Account to Liouville's Theorem we define
the number of point one unit volume of phase
space as density p, then account to this theorem
the density of point remain constant with time.
V
= :0
p = constant
(q +dq.p+dp)
C
↑p
(speed)
q
D
(q dq,p)

Expert Solution

Step by step

Solved in 6 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Given vectors a=(5,3) and b=(-1,-2) Find the x-component of the resultant vector: T` = 2 a + 36
Carbon dioxide gas, CO2, travels at about 340 m/s at room temperature. What is the travel rate (velocity) of helium, He, at the same temperature?
(0, 1, 0) is Consider a two-dimensional incompressible flow in the xz plane: u = - ey x Vo, where e the unit vector perpendicular to the xz plane. Denote the two velocity components in the xz plane as u and w in the x, z directions, respectively. Write down the expressions for them in terms of o. If the function of o assumes = x2² calculate the values of u and w at the coordinate x = = 2, z = 1. Ou= Ou= 86 əz > Ou=- - 86 əx W= ap dz 7 W= W= 8p Əz ap əz " ap " əI u = 4, w = -1 u = -1, w = 4 u = −4, w = 1 86 0₂7 86 Ou=- W=- u= -1, w = -4 5 dr =
The gas law for a fixed mass mm of an ideal gas at absolute temperature T, pressure P, and volume V is PV=mRT, where R is the gas constant. Find the partial derivative (∂P/∂V) (∂V/∂T) (∂T/∂P) = ?
4.2.1 The velocity components of u and v of a two-dimensional flow are given by u = ax + bx x²y² by and v=ay+ .2.2 where a and b are constants. Calculate the acceleration.