Hey everyone,
So I have had a lot of fun using Mathcad since Feburary of this year. Our FIRST Robotics Competition team 1671 from Clovis, CA got it free as a part of competitions Kit of Parts. I have main been checking out the solve and set equal to operators and taking integrals for my Calculus homework when I get tried of doing them by hand.
But recently, I have found another use for it. A little over a month ago, I joined the Zero Robotics Competition, a competition sponsored by MIT, NASA, DARPA, TopCoder, and some other institutions. They challenged teams to develop software that would make a robot revolve a round an object, like in a circle. Although it was quite simple at first, as the task got more difficult, I turned to Mathcad to help me solve some problems.
However, I recently ran into some difficulties. First off, I am not entirely sure what Mathcad does and does not allow and understand. I have no formal training; I mainly learn through the included tutorial files on the program (Mathcad 15.0).
In any case, I am trying to find the equation of the cirle where a sphere and plane intersect. I had realized, given the equation of the plane, and using spherical polar coordinates, one could determine the polar/zenith angle (ϕ, phi) given the azimuthal angle (θ, theta). When I use the solve operator for ϕ, I get an answer. But when I try to retrieve the relation used to solve ϕ from θ, I get an error.
I have attached my work thus far. Sorry the messiness!
polar_azimuthal takes the simple plane of y + z = 1 and use polar coordinates to determine the ϕ and θ that match. changing the value of θ will invoking f(θ,ϕ) to run and produce an answer for ϕ. pol_azi_2 tries to do the same thing, excepting using a general case.The final box equation attempts to solve for the relationship of ϕ and θ, but fails. I am guessing it's either dividing by zero, can't be factor, both, or something of the nature. I just don't know!
If you are able to find anything out, our team would greatly appreciate it!
Also, how can I use the arrays to simulate vectors and take dot and cross product?
Thanks!
Evan Giarta
FIRST Robotics Competition Team 1671 Buchanan Bird Brains
Zero Robotics Challenge Team ZRSC #49 Central Valley Manhattan Project
