Additionally note that crossing N with i is to get a vector perpendicular to N. \vec R(t) = \vec C + r\cos(t)\hat u + r\sin(t) \hat v
The parametric equation of the circle becomes: Normalize these two vectors to get \hat u and \hat v which are now orthogonal unit vectors in the plane of the circle. Let \vec u = N \times \vec i and \vec v = N \times \vec u. Go through the Cheat Sheet of Circular Motion and be familiar with different sub-topics like Newton Equation in Circular Motion, Centripetal Force, Net Acceleration, etc. To help you learn the concept of Circular Motion better we have listed the Circular Motion Formulas in an efficient manner. Let N = \langle n_1,n_2,n_3\rangle be the normal vector, \vec C = \langle a,b,c\rangle be the position vector of the center, and r be the radius. Circular Motion can be uniform as well as non-uniform. where g, f, c are constants and center is (-g, -f) and radius r g 2 + f 2 c. General Equation of the Circle : The general equation of the circle is x 2 + y 2 + 2 g x + 2 f y + c 0.
#Circle equation how to
Here's how to do that the algebra gets messy in the general case but not bad for specific numbers. The general equation of the circle and standard form of circle are given below with examples. I'm a little late to this thread, but as you have noticed, nobody has given an answer that contains only the three pieces of information posited by the original poster: The center, the radius, and a normal vector. How exactly do you derive vector U? its more complicated than just Rcos(t),Rsin(t) because you have that third axis, right? So in general we can say that a circle centered at the origin, with radius r, is the locus of all points that satisfy the equations. In order to factor the original equation, we will need to add a magic. "Where u is a unit vector from the centre of the circle to any point on the circumference" From the above we can find the coordinates of any point on the circle if we know the radius and the subtended angle. OUR GOAL: To find the standard form of the given circle equation by factoring.
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