## What initial conditions am I missing?...

I've been writing this code to simulate the orbit of Venus in a simple 2D polar plot, but it keeps telling me that I have insufficient initial conditions, here is the code:

restart:with(Physics):with(VariationalCalculus):with(plots):with(plottools):

R[V] := 0.72*AU: #`starting radius for venus`

AU := 1: #`astronomical unit`

G := 6.674*10^(-11): #`gravitational constant`

m[S] := (333*10^3)*m[E]: #`mass of the sun`

m[V] := 0.815*m[E]: #`mass of venus`

m[E] := 1: #`mass of the earth`

x[V] := t -> r[V](t)*cos(theta[V](t)): #`x-coordinate`

y[V] := t -> r[V](t)*sin(theta[V](t)): #` y-coordinate`

x[VP] := t -> diff(x[V](t), t): #` x-velocity`

y[VP] := t -> diff(y[V](t), t): #`y-velocity`

T[V] := m[V]*simplify(x[VP](t)^2 + y[VP](t)^2)/2: #`kinetic energy of the system`

V[V] := (-G)*m[V]*m[S]*1/r[V](t): #`potential energy of the system`

L[V] := T[V] - V[V]; #`lagrangian of the system`

EL[Vr] := diff(L[V], r[V](t)) - diff(diff(L[V], diff(r[V](t), t)), t) = 0: #` e-l for the r-coordinate`

EL[`Vtheta;`] := diff(L[V], theta[V](t)) - diff(diff(L[V], diff(theta[V](t), t)), t) = 0: #`e-l for the theta-coordinate`

EL[V] := [EL[Vr], EL[`Vtheta;`]]; #` system of equations`

F[V] := G*m[V]*m[S]*1/R[V]^2: #`gravitational force for venus starting position`

omega[V] := sqrt(F[V]*R[V]*1/m[V])*1/R[V]: #`angular velocity for venus starting position`

IC[V] := [r[V](0) = R[V], D(r[V])(0) = 0, theta[V](0) = 0, D(theta[V])(0) = omega[V]]; #`initial conditions, r-position, r-velocity, theta-position, theta-velocity`

SOL := dsolve(EL[V], IC[V], [r[V](t), theta[V](t)], numeric, output = listprocedure); #`numerical solution`

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

I have included both the initial values for r,dr/dt, theta and dtheta/dt.

I'm not sure what other initial conditions I could be missing?

## Optional Python installation?...

Currently, a stand-alone or embeddable Python is by default bundled with Maple and is installed silently (namely, without notification) when installing Maple, but why is there no prompt panel asking for Python configuration (just like Why does Maple ask for a Matlab installation when I install it? and Configuring the Maple Kernel for Jupyter)?
Actually, I am wondering why I am not capable of installing Maple without bundling Python (even if I am able to clear those files in \$MAPLE/Python.\$SYS later). In my opinion, a bundling Python suite is more or less unnecessary; wouldn't it be better to provide a tooltip asking for approval? If one really need to interact with Python, one may instruct Maple to make use of some available local version of Python from the outset (rather than having to install an additional Python interpreter with numerous extra packages that occupy almost 2 GB!), and if one does not require such a functionality, one can simply skip the Python installation and free up 2GB immediately. So, will installing Python (or another popular external program, if it is going to be integrated or connected with Maple in future releases) be optional during the Maple installation process?

## Reply to posts slow and sometimes not working...

For the past days I observe that reply to posts stucks at the progess bar

(using a firefox browser). I am wondering whether that is only on my installation. Loading pages is not slow as reported here. I have a suspicion that this happens after having previewed a reply before submission. I observe also sometimes a yellow background of the preview and sometimes a blue background.

I try to submit now with blue backgound

## Is maplev-mode still supported?...

Ubuntu 22.04.

I have Maple-202[1-3] and an old installation of maplev-mode. maplev-mode fails to work.

In the emacs messages buffer, I see (typed from memory):

maple not running

I removed all of maplev from my system.
make install fails:

> pwd
/tmp/maplev-master
> make install
Makefile:27: MapleLisp.mk: No such file or directory
make: *** No rule to make target 'MapleLisp.mk'.  Stop.

I tried installing from the cloud, but, failed. The error message (even run as root)

Error, (in PackageTools:-Install) permission denied

Will maplev-mode work?

Tom Dean

## I have a question about an arc error on the Variab...

To observe the nip impact of the Variable Nip Roller, we created the following schematic and simulation. I set the y-coordinate of the Web to be the same, so I don't think there is a big problem for the Variable Nip Roller to simulate the nip. However, the simulation does not simulate with the warning "Nip is not on the contact arc". What is the reason for this and how can I set the nip arc again?

## Questions about how my probe items differ from the...

This is a Tension Zone, an example of web handling.

The example probe on Roller1 shows various probe items, such as summary_WrapAngle and summary_Slipvelocity, but the ex_probe I attached to the same roller shows only four probe items: angle, angular velocity, angular acceleration, and torque. Why are the items different even though they are probes on the same roller?

## How can I get solution of this integral?...

Good day to all of you friends, just asking for your kind help.

I have been trying to get solution of the next integral but didn't have succes. The goal of the code is to perfom a variable change.

Best regards

## Error, (in dsolve/numeric/bvp/convertsys) too few ...

Boundary condition of my problem is   f(0) =1  and  d(f)(1) = -(k[f]/k[nf])*Bi*f(1).

But i am getting error when solve this.How to clear this .

my attached file is,

HNF_1.mw

## How to calculate time and memory ...

Dear Users!

I hope everyone is fine here. In the attached file I have solved a partial differential equation using the finite difference method for different mesh in spatial directions (i.e., for different Mx). I want to compute the time and memory to compute the solution against each Mx and want to plot it. Kindly help me how to compute the time and memory for each value of Mx.

TIME.mw

I shall be waiting. Thanks in advance.

## how do I solve and plot fractional differential eq...

I want a maple code to solve the caputo fabrizio differential equations using Runge Kutta method with implicit functions and impulsive conditions in maple. Is there any code structure for that.

## is this correct to solve the implicit fractional d...

restart;
with(Student[NumericalAnalysis]);
with(plots);
with(DEtools);
f := proc(u, r) local res; res := 1/25*r^2 + (sin(u(r)) + sin(diff(u(r), [r \$ 1/5])))/(r^2 + 47); return res; end proc;

RK4 := proc(f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u := Vector(n + 1); r := Vector(n + 1); u[1] := u0; r[1] := r0; for i to n do k1 := f(u[i], t[i]); k2 := f(u[i] + 1/2*h*k1, r[i] + 1/2*h); k3 := f(u[i] + 1/2*h*k2, r[i] + 1/2*h); k4 := f(u[i] + h*k3, r[i] + h); u[i + 1] := u[i] + 1/6*h*(k1 + 2*k2 + 2*k3 + k4); r[i + 1] := r[i] + h; end do; return [u, r]; end proc;
RK4 := proc (f, u0, r0, h, n) local u, r, i, k1, k2, k3, k4; u

:= Vector(n+1); r := Vector(n+1); u[1] := u0; r[1] := r0;

for i to n do k1 := f(u[i], t[i]); k2 := f(u[i]+(1/2)*h*k1,

r[i]+(1/2)*h); k3 := f(u[i]+(1/2)*h*k2, r[i]+(1/2)*h); k4 :=

f(u[i]+h*k3, r[i]+h); u[i+1] := u[i]+(1/6)*h*(k1+2*k2+2*k3+k4\

); r[i+1] := r[i]+h end do; return [u, r] end proc

u0 := cos(abs(0.9))/15;
u0 := 0.04144066455

r0 := 0;
r0 := 0

h := 0.1;
h := 0.1

n := 100;
n := 100

solution := RK4(f, u0, r0, h, n)

u := solution[1];
r := solution[2];
plot(u, r, style = line, color = blue, labels = ["Time (r)", "Solution (u)"]);
is this correct to solve the implicit fractional differential equations using 4th order Runge-Kutta Method. will fsolve command  solve the fractional differential equations ?

## how to define a gauge plus coordinate covariant de...

Hello
i am using maple 2023 and the physics package and have the following question:
I want to define a gauge-  plus coordinate covariant derivative i.e.
assuming i,j,k are SO(3) indices and greek indices describe 4-dim space-time (not necessary flat)
i need the following derivative:

D_sigma F_i _rho _lambda = nabla_sigma F_i _rho _lambda + epsilon_i ^j ^k  A_j_sigma  F_k~rho~lambda
with _ meaning lower indices and ^ upper indices and nabla the convenient coordinate covariant derivative of general relativity.
F is a tensor objekt with 2 space time indices and 1 so(3) indices (e.g. Yang Mills field strength) and A is the so(3)gauge potential
How can i define this Differentialoperator with the physics package.
I.e. i want to work with SO(3) Yang-Mills Fields in curved space time and need this generalized Differentialoperator
thanks for helping. I hope its clear from this ascii text in the screen
regards Michael

## Handling optional inputs to procedures?...

How should optional input parameters be handled for procedures. The example has three optional inputs

vars:=[x,y]   ,  clr:="b"   and prnt:="y"  . if one wants to change prnt to"n", vars and clr values must be entered.

{vars:=[x,y]  } , { clr:="b" }  and{ prnt:="y"}  this is a good method because one just enteres prnt="n".  But have to remember the input parameter name prnt.

I have a 3rd option, but it is to complicated and probably unreliable to use in practice.  and with more than 3 optional inputs too difficult to code.

I am wondering  are the other approaches and what is the prefered methodology. I have about 30+ procedures to apply this to in a package.

Edit:-  I can change the prnt to boolean true, false instead of "y" , "n".  That would make the all the optional inputs different types.

In Test1 its should be vars::list:=[x,y] not vars::{list , `string`}:=[x,y]

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# 3 This is possible but is a very complicated method of handling the optional inputs and difficult the handle altered sequence on inputs.

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## how to get plot for the exact solution of a piecew...

ow to get plot for the exact solution of a piecewise function and i need the correct plot which has curve started at y-axis (0.5) and goes till 2?