A video where balls roll along a curve without friction, attracted by a gravitational force. The brachistochrone is the fastest. The brachistochrone is modeled to be a part of the circular shape. So if you take it further, you get a perfect circle. The "sweep" is about 109°. A "sweep" of 360° achieves a complete circular shape. If the trajectory with the red ball is trajectory 1, and the trajectory with the dark blue ball is trajectory 5, the order from fast to slow is: 2 (brachistochrone), 3, 4, 1, 5. Trajectory 1 is a linear trajectory with an angled corner, trajectory 2 is a brachistochrone, trajectory 3 is slightly bent towards the gravitational source, trajectory 4 is a trajectory without curvature (linear), trajectory 5 is slightly bent against the gravitational source. The gravitational source acts downwards.
<p>Initial situation and progression: All the balls are lined up in an imaginary row, and they all start from the same height. They fall and roll along their respective curves and end up in the "catch basin" The tracks are equidistant from each other, the balls all have the same dimensions and physical properties.
</p><p>Physics: To realize this simulation, physical properties were applied. So the spheres are active "rigid bodies", the curves passive "rigid bodies". In order not to slow down the balls by effects, friction was removed everywhere, also the bounciness and damp(ing). The gravitational force was realized by a field to which the spheres react. The magnitude of the field is 9.8; approximately the gravitational force of the earth of 9.81 m/s².
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<div style="font-weight:bold;display:inline;" dir="auto"><img alt="Pictogram voting info.svg" src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Pictogram_voting_info.svg/15px-Pictogram_voting_info.svg.png" decoding="async" width="15" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Pictogram_voting_info.svg/23px-Pictogram_voting_info.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Pictogram_voting_info.svg/30px-Pictogram_voting_info.svg.png 2x" data-file-width="250" data-file-height="250"> Technical information</div> The bitrate was chosen so that you can also extract individual frames, and thus get frames of the highest quality. The frame rate of 120 FPS allows smooth playback even at half speed.
<a href="//commons.wikimedia.org/wiki/User:PantheraLeo1359531" title="User:PantheraLeo1359531">PantheraLeo1359531</a>
2022-07-19
<span class="int-own-work" lang="en">Own work</span>