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### Adding tangent (velocity) vectors to a plot of a space curve [duplicate]

I am just getting started with Mathematica and need help plotting tangential vectors to a 3D parametric function. I know how to do this in 2D but am unsure how to do it in 3D. Maybe I am using the ...
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### How to define the tangent gradient operator? [duplicate]

I would like to define a new differential operator that is the tangent gradient for a curve $\Sigma$. This is defined as $$\nabla_\Sigma=\mathbf{P}\nabla$$ where $\mathbf{P}$ is the projection ...
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### Draw Vector Tangent to Point on Parameterized Curve [duplicate]

I define the vector function $\vec{r}(t)$ by r[t_] = {t, Cos[t], Sin[t]} The command r'[t] gives the vector tangent to the ...
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### Using Manipulate, how do you display the points on the curve and the tangent vector? [duplicate]

I'm new to Mathematica and my assignment is very vague... I'm hoping someone can explain to me a bit more of that this quesion means: Given the curve C, display the point on the curve and the ...
3k views

### How to find the magnitude of a vector?

I'm doing this exercise in Wagner's book (p.78) , and this is my attempt: ...
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### Plotting a 2D shape along a 3D parametric function curve

Say I have a 3D curve that is parametrically defined. How would I be able to plot shapes like figure 8's whose centers are aligned along the 3D curve? Say the curve was: ...
903 views

### Computing Gaussian curvature

Can Gaussian curvature $K$ be computed from WolframAlpha or any other available Mathematica program? Please indicate the program or its reference. If input ...
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### Using the epsilon tensor in Mathematica

I'm having a great deal of trouble getting started on a weekly homework assignment in Mathematica. The assignment requires we use the epsilon tensor which is apparently built into Mathematica as ...
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### Solving the Frenet Serret equations for non-constant curvature and torsion, obtaining parametric equations

I wish to solve for the curvature and torsion functions $k_1 = \dfrac{1}{1+s^2}, k_2 = \dfrac{s}{1+s^2}$ using the Frenet Serret system and obtain the parametric equations for the curve. I need the ...
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### Drawing normals to a curve

I want to draw a series of normals to a curve, where the curve has been parametrized by a single angle, i.e., the polar angle. The curve is actually sinusoidal perturbation of a circle of radius 1/2,...
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### Simple Plot of Vector

I have a vector $<x(t),y(t),z(t)>$ constrained to a unit sphere. I am trying to plot what the vector looks like as time progresses. What would be the easiest approach to visualizing this? I ...
562 views

### Marking specific points on a 3D curve

Here is the curve below. (written as a position vector) r = {Cos[7 Pi*t], Cos[6.2*Pi*t], 2.5*t} ParametricPlot3D[r, {t, 0, 2}] I want to know how I can mark ...
I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by t(s)=\frac{\gamma'(s)}...