Consider a Euclidean space or a manifold or whatever. Furthermore, consider two regions on this space. If one can construct a diffeomorphism between the points from one region to the other, does this imply that the two regions are homeomorphic?
My gut feeling is "yes," but I would like a...
Perpetual motion is a misnomer. It means a system that can continuously give off energy ad infinitum. Of course, this violates the conservation of energy and is therefore impossible.
However, this does not stop people from selling "perpetual motion electric generators" to the uneducated.
If you think that a significant portion of physics formulay can be derived by "kinematics," then you are gravely illusioned. In addition, Serway does derive many of their formulas if you were to bother reading them.
All of the standard introductory physics books are the same; they are all...
Dimensionally, torque (moment) has the same units as energy. However, that alone does not give you permission to add these totally different quantities.
Mathematical Aspects of Classical and Celestial Mechanics by Arnold etc. (not to be confused with the textbook Mathematical Methods of Classical Mechanics by the same author) is clear, excellent, and encyclopedic. However, most of the proofs are missing and are to be supplied by the reader. Not...
Entropy is not just a measure of the disorder of position, it is also a measure of the disorder of momentum. As a cold dust cloud collapses into singularity (assuming Newtonian mechanics), the disorder ("chaos") in momentum increases.
Mathematically, entropy is a measure of area a bunch of...
Termina, that is not true. First of all, a two-body system acting via gravity NATURALLY is elliptical (or hyperbolic). The sun is not responsible for the Moon's elliptical orbit.
Ugh, this is absolutely discussing. An incompetent government must compromise their failures by attempting to stop dissenting conversation? Last time I checked, people cannot be withheld from (most) jobs based on political affiliation. Of course, it is not like the results of wiki leaks can be...
Let me clear this up why I differentiate poll and study using an example.
POLL:
"Are you gay?
[] Yes
[] No"
STUDY Questionnaire:
"1. Do you identify yourself as gay?
[ ] Yes
[ ] No
2. Are you in a relationship?
[ ] Yes
[ ] No
3. If you are strait, have you ever had homosexual...