2017 HiMCM A题特等奖学生论文下载8040

2017 HiMCM A题特等奖学生论文下载8040

 

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论文摘要如下：

2017 HiMCM Summary Sheet

The problem of sky display with Drone can be interpreted as designing visible and safety locus of drone lights to form image of three different objects, which are Ferries wheel, dragon, and a self-designed pattern (a smiling face) respectively. In this paper, we successfully developed a few comprehensive mathematical models to determine the number of drones required and model their initial location and the flight paths mathematically in both static and animate state.

We addressed this problem mainly through space coordinate frame which allowed us to formulate the motions of all the drones in all animations. In the first part, we designed the Ferris wheel as a composition of several geometrical shapes, a circle with spokes and two identical triangles. Considering the space coordinate of every points and using the idea of matrix, we constructed the model based that on the thought of substituting every points own coordinate with its consecutive former one in the same circular motion path.

In the second part, we made a two dimensional dragon that has detailed features such as head, tail, claw, and scale. We made the body of the dragon as the shape of sin(x), and the movement model was created, enabling the dragon to move smoothly and periodically during the animation.
For the third part, our team decided to create a calm face that would eventually turn into a smile face. We made a few functions to express straight lines that represent expressionless eyes and mouth were bent to a smile face by changing the coordinates of the points in the straight line to coordinates of points that fit in parabolas..

After finishing all three models, our team gave out the evaluation for each of them with MATLAB programming. Based on the calculation, we determined to use up to 427 drones to create three sky displays. And the required launch area would take up 9m×9m, and the air space of 100m in length, 50m in width and 80m in height was required. The duration for the light show would be 30 minutes.
In summary, our mathematical model could successfully determine the requirements for this aerial light show.

 

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