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I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$$${\bf x}(t) = r(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.

I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.

I am trying to plot a function $${\bf x}(t) = r(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.

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I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.

I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.

I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.
I am trying to plot a function $${\bf x}(t) = a(t)\hat{v} + {\bf b}(t)$$, with unit vector $$\hat{v}$$ and vector $${\bf b}(t)$$ given in spherical coordinates. For simplicity, assume that $$\hat{v} = (\sin\theta\cos\phi, \sin\theta\sin\phi, \cos\theta)$$, and $${\bf b}(t) = [t, \sin(a+t), \cos(b + at^2)]$$, where $$a$$ and $$b$$ are constants. This is easy to plot, however, I want the angles $$\theta$$ and $$\phi$$ to satisfy an implicit equation, say, $$\cos\theta + a(\phi + b t)^2 + c = 0$$.