Rotating reference systems, apparent forces
This program is designed to illustrate centrifugal force and Coriolis force. These apparent forces only occur in rotating reference systems, but are often wrongly assumed to also occur in stationary systems. This program can be used to switch between a description in a stationary system (blue coordinate cross) and a description in a rotating system (red coordinate cross). As an example movement, the trajectory of a body with the mass m is tracked on which a radial force F acts with selectable distance dependence. The strength of the force and initial conditions for the movement can be set. The default setting is the example of a circular movement. All forces on the body are drawn as arrows during the movement. The specified force F, which acts equally in both reference systems, is shown in blue. The centrifugal force (pink) and Coriolis force (red) naturally only act in the rotating reference system. This becomes obvious when switching between the two reference systems during the movement. Some frequently used examples (circular motion, deflection in free fall, Foucault's pendulum) can be illustrated by selecting the appropriate parameters. However, more complex movements (elliptical path, straight-line uniform motion, etc.) can also be investigated. In some cases, amazingly complicated paths are observed in the rotating reference system.
Operation
After opening the program, a movement with preset parameters can be started using the start button. The blue coordinate cross always represents the stationary reference system(x to the right, y upwards). The red coordinate cross represents the rotating reference system. The selection in the top left-hand corner can be used to switch between the two reference systems. From the point of view of the stationary system, the rotating (red) coordinate cross is also displayed. From the perspective of the rotating system, i.e. a co-rotating observer, only the red coordinate cross is displayed. The angular velocity omega at which the system rotates is entered at the top left. Below this, the force law to be used is set and the parameter a for the strength of the force is entered. The force F always acts in a radial direction(a>0 outwards, a<0 inwards). Furthermore, the mass m of the body and the initial conditions, i.e. the components of the starting location and the starting speed, can be entered. The initial conditions refer to the location and speed in relation to the stationary reference system. The image section can be set with "Zoom" (approx. 1m to several 1000m) and the display of the force arrows can be adapted to the image size with "Arrow length". The display of the force arrows can also be switched off completely (bottom left). If the calculated path curve of the body consists of more than 10,000 individual points, the program is automatically stopped. The coordinates of the point in the currently selected reference system are displayed at the cursor. If a parameter is changed, the movement is stopped and must be restarted.
Numerical realization: The trajectory of the mass is calculated in the stationary system with 4th order Runge-Kutta at a step size of 10 µs (actually much too accurate). The image is drawn completely every 50 ms. In a rotating system, all points are converted by applying a rotation matrix. The force arrows are calculated analytically from the current path parameters (location and speed).