- #1
Pencilvester
- 196
- 46
How would I go about solving for ##t_p## in the following equation:$$t_p - t + vy \cos {(2 \pi \omega t_p )} - vx \sin {(2 \pi \omega t_p )} = 0$$where our input is a point in ##ℝ^3## with coordinates ##t##, ##x##, and ##y##, and where ##v## and ##\omega## are constants. I’m pretty sure it can’t be a function exactly, as I’m pretty sure most, if not all input points will each yield 2 distinct outputs. If it matters to you, ##|v| < 1##, but I don’t think that it’s relevant to this problem. And this isn’t any kind of homework problem. I’m not in school, I’m just trying to analyze what a coordinate transformation might look like for going from coordinates of an inertial observer in flat spacetime to coordinates of an observer tracing out a helix in spacetime (or a circle in space), and I’m running into this limitation in my mathematical abilities, so any help would be much appreciated.