I run into a problem that really suprised me. I have a program that solves a system of differential equations with different initial conditions. I wrote a cycle that goes through initial conditions, solves differential equations and saves the picture (displaying dynamic behaviour of the system) in the given directory. All seemed fine and working until I once checked one of the pictures by running the program on the only one initial condition. It turned out that the picture program gave me this time is not the one that program gave me earlier (while running through cycle). So I panicked and started checking other pictures and it turned out that some of them are right and some of them are not, remarkably, with no particular pattern.

I reckon that I somehow need to manage the memory, clear it after every iteration. (I'm not absolutely sure that problem is here but I just don't have another explanation why this thing could happen.)

File:ClassicalTrajectoriesH2X_morse_pictures.mw

I'm modeling the interaction between rotation and vibration in water molecule. I've come up with the solution functions, but I wanted to make some illustrative animations to fully understand what is going on. I made an animation (in the very end of the attached file) showing vibration of molecule and I want the trajectory of each (of two) particles to be traced after it, how could it be done? Also I want to have the movement of the angular momentum vector (vector with components [Jx=J*cos(varphi)*sin(theta), Jy=J*sin(varphi)*sin(theta), Jz=J*cos(theta)]) be animated simultaneously with the vibration of molecule (on the same plot). Is it hard to achieve?

File: ClassicalTrajectoriesH2X_morse.mw

I'm sorry for asking too many similar technical questions, but I just can't help this.

I'm solving a system of differential equations with dsolve and getting this type of error:

Error, (in f) unable to store 'HFloat(0.10664489706950975)+HFloat(1.1891638418458722e-5)*sin^2-HFloat(1.6095871822513048e-6)*sin' when datatype=float[8]

I checked the dsolve syntax, checked that all the constants are defined, checked that the number of equations matches the number of unknown functions (and there is no misprints of them in the code). In brief, I checked all the stuff that I usually have mistakes in, and yet the error stands. 

Here's the file: 1.mw

I have a number of dots that lie on the sphere. I want to draw a handsome sphere with three axes, put dots on the sphere and connect them. The problem is that some dots are pretty far from the other and so the line connecting them goes under the surface of the sphere and so is not seen. Therefore the question, how the dots can be connected so the line would be seen (or the line would lie on the surface of the sphere)?

Here's the file:ClassicalTrajectoriesAr-CO2.mw

I'm trying to solve vast system of differential equations (Hamiltonian equations of motions). 

I have this kind of error and don't know what to do with it:

Error, (in dsolve) found the independent variables {t} also present in the names of the functions of the system {(cos(varphi(t)))((3333333333/10000000000)/sin(theta(t))^2+(1/23)*cot(theta(t))^2/R(t)^2), (sin(psi(t)))((3333333333/10000000000)/sin(theta(t))^2+(1/23)*cot(theta(t))^2/R(t)^2)}

Here's the file:ClassicalTrajectoriesAr-CO2.mw