The symmetric group Sâ?? operates on two sets U and V of order 3. Decompose the product set UÃ?V into orbits for the diagonal action g(u,v)=(gu,gv), when

a) the operations on U and V are transitive,
b) the operation on U is transitive, the orbits for the operation on V are {vâ?} and {vâ??,vâ??}.

The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest or

The muon is a subatomic particle with the same charge as an electron but with a mass that is 207 times greater. m_u = 207m_e. Physicists think of muons as "heavy electrons". However, the muon is not a stable particle; it decays with a half-life of 1.5 microseconds into an electron plus two neutrinos. Muons from cosmic rays are s

Assume that the earth and the moon have circular orbits (which is almost true) and that the periods of their orbits are 365 days and 28.0 days, respectively
How much work does the earth do on the moon in one day?
W(earth)= ? J
How much work does the sun do on the earth in one month?
W(sun)= ?J

Please see the attached file for full problem description.
A bead is placed at each of the six vertices of a regular hexagon, and each bead is to be painted either red or blue, how many distinguishable patterns are there under equivalence relative to the group of rotations of the hexagon?
Repeat Problem 8 with a regular h

Haley's comet orbitsthe sun every 76 years, and was first observed in 240bce. Its orbit is highly elliptical, so that its closest approach to the sun (perihelion) is only 0.587 AU, while at its greatest distance (aphelion), the comet is 34.39 AU from the sun. (An AU, or astronomical unit, is the distance from earth to the sun,

For a circular orbit around a massive gravitating body, the speed depends on the radius according to Equation 8.3; for elliptical orbits, the speed varies according to the equation V squared=2GM{(1/r)-(1/2a)}, where r is the distance from the massive body and a is the semi major axis of the ellipse(i.e., half the sum of the clos

The spectrum of hydrogen with a nucleus of ﬁnite mass. The analysis in Section I-7 of the text assumes that the nucleus remains ﬁxed as the electron orbits about it. This corresponds to assuming that the proton mass is effectively inﬁnite. More correctly. we should picture the proton and electron as orbiting about their co

NOTE: This may be more of a "non-linear dynamics" problem than an ODE one.
Here goes...
I've recently been toying around with this system:
x' = y*e^{-(x^2+y^2)}
y' = -x*e^{-(x^2+y^2)} // (where "e^" denotes the exponential function)
I've noticed strange behavior that I can't seem to explain. I used a progr