This function plotter displays animated orbits in 3D space. Three functions for the space coordinates map the continuous points on the number line of the one dimensional variable t unambiguously to a point in space xyz.
After the start of the animation at t = 0 the variable t increases linearly in time to create a moving point. Its trace in xyz space is recorded as its trail. The moving object itself is shown as a moving dot at the head of the trail.
The functions may contain 4 parameters a, b, c, p that can be changed by sliders. In the predefined functions p is used for time control and hence determines the speed of the object..
At the Start of the simulation you will see a dot performing a linear−linear (arithmetic) spiral in space, viewed under perspective distortion. It is embedded into an xyz tripod, and is accompanied by the xy-plane z = 0. This plane can be deactivated by its check box.
Other predefined surfaces in space can by selected in the ComboBox.
The program calculates the functions in time intervals of ∆t = p*0.1 milliseconds. Slider p defines the speed of the movement; p = 0 stops it. Time t itself is shown in a number field in seconds. Start resets t to 0.
Sliders a, b, c vary the parameters between 0 and 1 in steps of 1/100 of an integer. This ensures that the quotient of parameters is a rational number − enforcing closed Lissajou traces. In one of the predefined functions the non rational number √2 is added, which leads to non closed trails. The parameters can be varied while the animation is running.
When you choose a function type in the ComboBox, its coordinate functions are shown in three formula fields x, y, z . You can edit the formulas or input completely new ones for an unlimited number of possible variations. Do not forget the ENTER key after changes!
Pause freezes the animation, Play continues it.
There are two buttons to start the program, with different visual results.
Start clears all traces and starts calculation at t = 0.
Play leaves old traces and superimposes new traces for other parameters or for another type of function.
Clear clears traces without stopping the animation.
Reset a b c restores a b c to the default values without clearing traces.
The range of all three axes is ∓1 . The xy-plane is at z = 0. Minimum and maximum values of z are marked by a green and a red dot. The calculation is stopped when one of the coordinates gets out of range.
The orientation of the tripod in space can be changed by drawing with the mouse.
Other ways of visualization are described in the next page.
Values of a marked point in the curve are shown in the left lower corner when the Alt key is pressed.