# All Questions

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### How to derive trigonometric Cartesian equation from parametric

How can one derive programmatically a Cartesian equation when $x$ and $y$ are parametrically represented by trigonometric functions? i.e.: Given that $x= \cos(2 t)$, and $y = -\sin(t)$, how can I ...
49 views

### Solution to non-algebraic equation with parameters

I have to solve the following equation a Tanh[z-b] = z, with a and b parameters and ...
248 views

### Find multiple solutions of a nonlinear ODE

I have a nonlinear ordinary differential equation with two parameters c and R in the form of: ...
53 views

### Area of a parametric plot with interpolating functions

I am looking for the area of a parametric plot defined by two solutions (defined as: VVLt & PVLt) of Numerically solved differential equations. The problem is when i'm trying to integrate the two, ...
52 views

### Label curves with corresponding parameter

How can Plotlegend label each curve with the corresponding value of parameter param in the code below? ...
67 views

132 views

### Eliminating a variable from two expressions [duplicate]

I have the following equations - T = (2*cos[α]*sin[β])/sin[α + β]; sin[α]/sin[β] = sqrt[1 - V/E]; And I want to eliminate β ...
206 views

### Find parameterized intersection curve of two parametrized surfaces

I am more or less new to Mathematica, but have never dealt with more complex problems requiring more advanced coding and would be grateful for some guidance. I have got two parameterized surfaces, ...
411 views

### Transforming the parametric equations of a curve into an implicit equation in Cartesian coordinates

I have a parametric curve defined by x = 2 Sin[t] + Sin[3 t] y = 2 Cos[t] - Cos[3 t] How can I eliminate t so get a single ...
151 views

### Add two functions in a table with the same variables

How can I print the values of the function expere in the table of the function exper ... Note that I use this code ...
29 views

### Groebner bases with symbolic exponents [duplicate]

I'm trying to eliminate variables using Groebner bases or polynomial resultants with symbolic exponents. I'm wondering if it is possible to do it in general case for non-negative integers $C_{ij}$. ...
192 views

### Solve for parameter in ParametricNDSolve

I have a simple 2-variable ODE system with a parameter $P'[z] = -2\Phi[z]$ $\Phi'[z] = -2\frac{P[z]}{a}$ I've implemented the code as follows ...
78 views

### How to use one of the results of a parametric function as a new function with the parameters as variable

I would like to use the result of a parametric equation as a new function of the parameters. Given the solutions of the following ...
200 views

### Eliminating variables from system of equation using Eliminate or Solve

I have a system of equations for algebraic curve given by the zero locus of some polynomial encoded in the system of equations (I want to eliminate variable z and get algebraic curve in terms of x and ...
128 views

### Relation between two variables in a function

I have a function, say F1[θ1_, ϕ_] = Sin(θ1 + ϕ) + Cos(θ1 + ϕ) and another function F2[θ2_, 2ϕ_] = Sin(θ2 + 2ϕ) + Cos(θ2 + 2ϕ). ...
466 views

### ParametricPlot3D Self Intersection

I would like to know where my ParametricPlot3D intersects itself and to extract all intersections (points, lines, surfaces...) to animate them by changing ...
121 views

### Derivative ParametricNDSolveValue

i'm work with heat conduction in cylindrical coordinates, my problem is how to calculate a derivative for a parameter using ParametricNDSolveSolution. ...
671 views

### Find Where a Parametric Equation Overlaps [duplicate]

I have a parametric equation: r[t_] = {2.9 Cos[3.2 Pi t], Sin[4 Pi t] + 5 t}; which overlaps at a point in the $\{-x, y\}$ region of a plot. I'm trying to ...
555 views

### Finding the intersection of two parametrised functions

I have a Mathematica Notebook for drawing an evolute (involute) like this: ...
281 views

### Finding “nice” solution for under-determined system with constraint?

Consider the following equation: ...
387 views

### Finding and plotting a parametric solution to a complicated equation (transcendental, log-polynomial)

I am trying (desperately) to find a way to solve a transcendental equation whose solution $x$ depends on non-numerical parameters $a$ and $b$. And then to produce a ...
77 views

### Numerically parameterize portion of $F[x,y]==0$ [duplicate]

I have a relatively complicated function of two variables F[x,y] whose zero locus contains a number of intersecting paths in the $x,y$-plane. A problem I've been ...
235 views

### How to speed up Solve command in Mathematica 8.0?

I have two complicated mathematical functions $f(s)$ and $g(M)$ that are complicated functions of $s$ and $M$ respectively. I would like to solve the equation $f(s)=g(M)$ in order to plot $s$ vs. $M$. ...
175 views

### Transforming from implicit Cartesian form to a parametric form [closed]

First equation $((1.2 x)^2 + (1.4 y)^2 - 1)^3 - (1.3 x)^2 y^3 == 0$ I wanna transform it into a parametric equation. I spent a much of a day working on it without success. The equation describes the ...
100 views

### Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
254 views

367 views

### Solve a function to find the optimum value of parameter in mathematica [duplicate]

I have a complicated function as shown It doesn't have a standard integration as far as I know. Now, numerical integration of the left hand side function over a set of points gives the right hand ...
282 views

### How to change parameters to equations of physical properties they belong to in an equation?

First off, I want to apologize for my poor English as I am not a native speaker. In my physics research, I had to solve a system of equations, from which I would get a solution for the speed of an ...
455 views

### Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
1k views

### Finding intersections of two parametric curves

I am dealing with the root finding of two parametric data curves (data below). I have already checked Parametric Interpolation of 2D data, which I found useful for plotting, though it is not adequate ...
218 views

### Sign of a symbolic expression as a function of parameter values

I need to know the sign of the following expression for p[t] = z/(1-a), as a function of the parameters {a, b, c, z}: ...
549 views

### How to convert a system of parametric equations?

I have a system of parametric equations (t is a parameter) ...
595 views

### How to Fit experimental data with 4D ParametricNDSolve?

Let me first explain the background problem. I'm trying to solve a problem with a projectile motion in 4D such that the position vector is: $\boldsymbol{r}(t)=\boldsymbol{r}[x(t),y(t),z(t)]$ I have ...
74 views

### Solve on parametric equation produces inequal results

I have a parametric (parameter t) equation in two dimensions (vectors). s = Solve[pt[t] == qt[t], {a, b}] Both pt and qt are parametric lines using a and b as ...
748 views

### Eliminating parameter from parametric equation [closed]

In Mathematica Online I tried: Eliminate[{x == t + t^3, y == t - t^3, z == 1 + t^4}, {t}] ...
236 views

### Finding roots of a function with a varying parameter

So I'm brand new to Mathematica, and basically what I want to do is find the roots of a function at varying time intervals. The function I'm using is: ...
732 views

### Solve a system of parametric equations

I have a system of parametric equations (with a total number of 8). I tried to solve this system by using Solve. I have not received an answer after about 4 hours! ...
I have the following parametric equation $$x^2-a=0$$ where $a$ is a given parameter. I would like to plot the nonnegative real root ($\sqrt{a}$) using NSolve as $a$ varies from $0$ to $1$. Can ...