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About `hýsøŕ

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  • Favorite Area of Science
    Theoretical Physics
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    2nd year T.P student
  1. you told me how to solve the physical problem with a particular boundary condition, but then the equation you gave would just be the one i posted rearranged slightly.. i mean how do you then solve the one you showed me with 0.5ml(d&/dt)2 = mgcos(&) + Constant ? without a boundary condition that is, for generality. @ajb yeah i guess it shouldnt perform s.h.m if you imagine a pendulum hehe, i was planning on trying to solve d^2 θ /dt^2 = -g/l sinθ around θ=pi/2 to see what happens when its at 90 degrees and falls but when i expanded it around pi/2, i get like..
  2. nono my question isn't how to solve the physical problem, i just want to know if the equation itself, d^2 θ /dt^2 = -g/l sinθ is directly solvable. like suppose you ended up with that equation in some completely different physics problem. since i posted this i tried wolfram alpha and it gives me some new function i've not heard of, namely the jacobi amplitude function, so i guess it does kinda exist and i'd just have to learn more about jacobi functions first ... so sorry this seems kinda redundant now lol
  3. Hai all, so in the usual pendulum problem where you have ... well a pendulum swinging from side to side under gravity, you end up with d^2 θ /dt^2 = -g/l sinθ where θ is the angle from the vertical axis, g is acceleration due to gravity, l is the length of the pendulum and t is time. now usually when you solve this, you have to use the small angle approximation on the sinθ so that the eqn turns into d^2 θ /dt^2 = -g/l θ which is rly easy to solve, but my question is, ... before you use the small angle approximation, can you solve the equation analytically and get some ki
  4. You haven't presented any sort of mathematical framework in which to explore this theory, so you aren't really able to make any quantitative predictions which could be testable and could falsify the theory. Physics, especially theoretical physics and in this case relativity/gravity relies on mathematics, and usually the mathematics of manifolds and differential geometry. here you have explained qualitatively some ideas you have about gravity and how it works, your thoughts about general relativity and things. but note that general relativity has had a large amount of experimental support,
  5. things like these that makes me wish we all had incredibly powerful brains, so I could understand the whole idea at the age of like 20 ish xD
  6. OHH i see, that's an interesting idea imo, thanks. i've heard string theory also predicts branes of higher dimensions, im guessing those would be target manifolds of higher dimensions? like the curve thing, only instead of a line it'd be like a sheet or a volume or.. uhh .. .. something (?)
  7. umm, i sort of see .. don't quite get much of this though, like what is the configuration manifold? also why the mapping or the target/source thing .. i don't see where all this stuff comes from
  8. @ajb interesting equation o.o haven't heard of this before, btw what do you mean by sigma models? :S @studiot well, here's roughly what i did: here's a derivation of the usual wave equation (for reference sake): http://www.math.ubc.ca/~feldman/m256/wave.pdf about the start of the second page, it's explaining how to get those cos's and sin's in terms of the derivatives of u(x,t). after this it goes on to make the small vibrations approximation where they use the small angle approximation with theta. So i tried to start off back with all thsoe cos's and sin's and use a different ap
  9. @ajb this sounds kinda beyond me tbh lol, i'll take your word for it at least for now @studiot well i tried working out what the wave equation would be, if instead of the approximation of small vibrations, the opposite (namely large vibrations) was used, but i get an unsolvable different equation :S the equation might not be completely unsolvable but i sure as heck can't get it lol, not even convinced its the right equation, but here it is just for the record: (dy/dx)^3 d^2 y/dt^2 = (T/ρ) d^2y/dx^2 .. T and ρ are constants also with the partial derivatives, aren't they partials be
  10. i was looking at the official string theory site, over here http://www.superstringtheory.com/basics/basic4a.html, and in the page i linked there it says that the idea of a string uses the usual wave equation, namely d^2 y/dt^2 = v^2 d^2 y/dx^2 (d's are meant to be partials) i remember when i was learning about the wave equation, its derivation involves use of the approximation that there are small vibrations, as it simplifies the differential equation into the one above, instead of a much more complicated non linear one. now if this equation is used to help define the physics of a string
  11. are you saying like... take a square, 2d, you could curve its surface by warping and bending it in the plane it lies in, without having to warp it 'up' into a third dimension (say, perpendicular to the plane the square lies in before its warped)? and that this is whats happening with our 4D spacetime? (i hope you guys get that this isn't easy to imagine lol)
  12. the shell analogy i have one clarification question for, namely does the idea that those spots getting further away from each other modelling the galaxies in our universe mean that our universe is expanding when observed from a 4+ dimensional space? (since the spots on the shell are being viewed from a 3 dimensional space and they're effectively on a growing 2 dimensional ring) ty for dis analogy it does help a bit i guess, a little clearer than the balloon analogy which has caused me much confusion over the years
  13. @enthalpy astronomy does sound rather interesting, structure in the universe is a fascinating topic imo, nice to see the complex processes that happened in the stars that gave rise to us and pretty much everything else known. however i was hoping on being the type of physicist that tries to construct or add to theories and things, as opposed to one who uses the existing ideas about relativity and things to investigate things in the universe, though that doesn't sound like a bad idea tbh. also the electric insulation would probably require me to know lots about electronics which i find really u
  14. @ajb nuclear physics is a big topic? i always just thought of it as a bunch of nuclear reactions you have to memorize :S @enthalpy well i was hoping on doing something at least partly related to unifying quantum mechanics and gravity, though nuclear and condensed matter seem .. sort of interesting too, perhaps i could do a bit of both :/ black holes also sound rather interesting. QCD, QED and stuff like that look interesting mainly because they look really mathsy, and i've found quantum mechanics to be so weird and wonderful xD nice to have all this choice available though
  15. ah thanks, those do sorta make the options seem a lot more open than just 'string theory or bust' xD and yeah i meant there that im entering the second year of a 4 year theoretical physics degree in a few months time.
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