# Studying simulation through making model of falling leaf[^dcl]:

## Group 14
* Yun-Chen Tsai, Department of Physics, National Taiwan University
* You-Cheng Zhong, Department of Physics, National Taiwan University
* Shao-Wei Wang, Department of Physics, National Taiwan University
* Che-Wei Pai, Department of Physics, National Taiwan University

## Abstract
Leaf falling, one of the simple phenomena around us, always becomes a representative of autumn's coming. To study the technique of building up a simulation, we take this simple phenomenon as a target, and try to build up a physics model to describe it. We will construct the model by viewing the leaf as the integration of "point-mass"-spring system with Python. We expected we can establish a model through this kind of approximation and have a "real leaf" in computational world. To check our simulation, we will compare the trajectory of leaf falling in our model with which in the video we shot. After testing the simplified model, we may be able to construct more complicated one, like different shape or with more kinds of force imposing on it rather than just gravity.

By studying deeper in the leaf-falling model, we expected that the way we take to establish the model can also be applied on different targets, such as the bat when hitting the ball or the motion of rubber band.

## Background and Objectives

Since the progressing of computer, it's possible for us to construct a "reality-like" model in virtual world. Not only in the field of Physics like what theoratical astronomers do to simulate how the stars born, but also, in video-game industry, such kind of ability also brings a revolution, builds up a wonderful virtual world for people to enjoy !

By building up a system with muitiple point masses and springs to describe the structure of leaves, it might be able to use this kind of "model-leaf" to precisely simulate how the leaf moves in real world. We would like to test if it is possible for us to create a "real-leaf" through this kind of approximation in computational world.

### Method

In order to determine the initial condition, we consider the state that the leaf is glued on the branch and the wind impose forces on it.

1. First, to construct a concrete imagination of how leaves fall, we use ellipsoid object in $\large{Vpython}$ .

2. Then, we establish simple system with few point masses and springs to roughly simulate the leaf, and we can consider more complex situation based on the simple model .

3. Eventually, we can compare the results from the model and the reality. To check our simulation[^lhsq],the trajectory of leaf falling in our model will be compared with which in the video we shot.

### Timetable

|Week|Date |Task |
|----|---------|------|
|1 |11/17-11/23|Reading papers and discussion.|
|2 |11/24-11/30|Designing poster layout.|
|3 |12/1-12/7|Developing a model for flat-ellipsoid shape leaf |
|4 |12/8-12/14|Comparing with the leaf in reality|
|5 |12/15-12/21|Modifying the model|
|6 |12/22-12/28|Check the model and try to apply on more complicated system|
|7 |12/29-2022/1/4|Collecting the data and preparing for the poster|
|8 |1/5-1/11|Checking the final version of poster|

### Responsibilities
1. Reading papers and discussion - All members
2. Design the poster - All members
3. Chair of weekly meeting -Y.C. Tsai
4. Programming - Y.C. Tsai, Y.C. Zhong
5. Data analysis and checking the model -C.W. Pai, S.W. Wang
6. Write the poster- Y.C. Zhong, C.W. Pai, S.W.Wang
7. Keep kind and Cooperate - All members

## Expected Difficulties and Solutions
1. The technical problem like taking a great approximation for the system might be disturbing, the possible way to solve this kind of problem we thought is to start from the simplest system and then go further steps by steps.

2. As our final objective is to create a "real-leaf" in computational world, the shape of leaves is inevitably needy to be considered. But basically, we can still consider some simple shape like a sphere at first, and then try to modify the model by comparing the statement in real world and virtual world.

## Expected Results and Evaluation

1. We expected we can establish the leaf-falling model that would be capable of describing leaf's behavior in reality.

2. By constructing the model of falling leaf, we might be able to give a easy example for the method of building up a complicated simulation.

3. The computer's ability may cause a great impact on the time consumed, which will make a huge difference on the performance.

## References
[^dcl]:Daniel C. Lluch, Analysis of the Out-of-Control Falling Leaf Motion using a
Rotational Axis Coordinate System
[^lhsq]:Li Haiyan, Sun Qingjie 、 Zhang Hui 、Zhang Qin , Example-based Motion Generation of Falling Leaf