The article theoretically analyzes the relevant knowledge of shot put in the shot put sports training of colleges and universities. The fractional differential equations are used to analyze the influence of the initial speed and the shot situation on the performance of the shot put. We obtain the joint angles of each stage of the shot throw through experimental design, time-consuming, final speed, limb displacement, shot-put shot speed, height, angle, and other kinematic parameters, and the shot-put motion trajectory of the picture stroke of the relevant action characteristics.

#### Keywords

- Fractional differential equation
- Shot put training
- Best shot angle
- Experimental simulation

#### MSC 2010

- 34A08

If the air resistance is negligible, we will throw the object obliquely upward at a certain rate. What is the farthest distance when the elevation angle is? The answer in middle school physics is 45°. The situation is different when putting shot puts. The throwing point of the shot is not on the ground but at a height above the ground [1]. In the sports-related instruction book, only the best projectile angle is 38°–42°, so it isn't easy to guide sports training correctly. Students cannot integrate theoretical models with actual sports. According to the projectile theory, this paper makes a theoretical calculation and analysis on the shot's movement [2]. At the same time, experimental simulation verification and discussion were carried out.

Approximate solutions in differential equations and parametric equations for calculating the best throwing angle [3]. From Figure 1, we can see that if _{y}_{x}_{y}_{x}_{y}_{x}_{x}dq_{y}_{x}_{y}_{x}_{x}dq

The integral on both sides can be obtained

So there is
_{0} = tan _{0} = tan _{x0} = _{0} cos _{0} are the angle and initial velocity of the throw, respectively.

Equation (2) can be abbreviated as

From equation (4) and _{y}_{x}

In the formula, the constant
_{0}, _{x}_{y}_{x}_{y}

In general, it can be assumed that the air resistance at the initial moment is a small amount compared to gravity [4]. That is, there is
_{(q0)} substituting _{0} = tan

In the rising phase, _{0}. Since _{(q)} is an increasing function of E when _{(q)} < _{(q0)} < 2.3.

In the descending stage, |_{(q)}| is negative, but even |_{(q)}| is only 9.8. Therefore,
^{m} ≈ 1 +

Although the above is a computational approximation, it is impossible to obtain a direct relationship between _{x}_{y}_{(q)}. The relationship between _{x}_{y}_{x}_{y}_{x}_{y}_{y}_{x}

_{x}_{(q)} is substituted into formula (1) to obtain

The integral on both sides can be obtained

Function _{(q)} consists of two parts:

Formally, the relationship between

Integrate both sides to get

We can get

Among them, _{(q)} is a function introduced for the convenience of writing [7]. It appears in the second part of the integral

So
_{(q)},

Substituting into the above formula and simplification appropriately

So far, we have derived the exact expressions (5) and (6) of _{x}_{y}_{x}_{y}_{0}, _{x}_{y}

Assuming that the horizontal distance between the landing point and the throwing point is _{1} + _{0} = _{0} = tan

When the basic parameter _{1}, _{0},

High-speed photography is often used to record movements in sports biomechanics research. At the same time, we use instruments to measure the relationship between force, speed, acceleration, and joint angle changes [9]. It is processed by force analysis, computer processing, and other methods. In general, high-precision instruments cannot be used for measurement. For this reason, we designed a simulation experiment: the use of fluid jets to simulate the projectile's movement to simulate and fit the actual movement of the shot to reflect the real movement of the projectile indirectly. This verifies the feasibility of theoretical calculation and analysis.

Experimental simulation of the projectile motion of the shot put requires the design of experiments by determining some parameters such as the object's initial velocity and initial height. Speed control is shown in Figure 2.

The height of the selected water outlet is also zero. The liquid surface velocity is zero. The height difference between the water outlet and the liquid surface is h'. The air pressure between the water outlet and the liquid surface is atmospheric _{0}. It is obtained from the above formula

In the formula _{0} is the water outlet flow rate (ie, the initial velocity of the projectile) and

Table (0.8m high), 2 elevated platforms (one is about 1m high, and the other is about 0.8m high). Elastic rubber tube (about 2m in length), clean ballpoint pen jacket (about 0.3cm in diameter). Protractor (inner radius 5), meter ruler, bucket, and clean carpet.

1) We insert the ballpoint pen jacket into one end of the elastic rubber tube as the water outlet to make an easy jet. 2) Place the bucket on the elevated platform and fill it with water until the water surface is flush with the upper port diameter of the bucket. 3) Insert one end (water inlet) of the non-ballpoint pen jacket into the bucket. The water outlet sags to a certain height (here, 0.8m is chosen) to be close to the table's edge as the water outlet point.

1) Insert the water inlet into the bucket, and let the water outlet fall freely. When the water flow is normal, plug the outlet end and prepare for the experiment. 2) Use a protractor to control the ballpoint pen jacket to select the water outlet angle. It shoots out from a height of 0.8m. 3) To prevent inaccurate positioning of water splash, we choose a clean carpet to spread on the experimental site. Use small objects to mark where the waterfalls and record them. 4) Use a meter to measure the horizontal run length of the water flow. Adjust the height of the liquid level for the next round of experiments.

The experimental data are shown in Table 1 and Table 2.

Test data 1

Experiment number | Height from liquid level to outlet h′/m | Ejection height h/m | Exit velocity v0/(m·s^{−1}) |
---|---|---|---|

Experiment 1 | 1.473 | 0.8 | 5.373 |

Experiment 2 | 1.008 | 0.8 | 4.445 |

Test data 2

Experiment 1 | Exit angle α/(°) | 25 | 35 | 38 | 40 | 45 | 50 |

Outgoing distance s/m | 2.324 | 2.437 | 2.5 | 2.36 | 2.726 | 2.23 | |

Experiment 2 | Exit angle α/(°) | 20 | 30 | 35 | 40 | 45 | |

Outgoing distance s/m | 1.77 | 1.815 | 1.82 | 1.754 | 1.73 |

It can be seen from Table 2 that the best spray angles of experiment 1 and experiment 2 are about 38° and 35°, respectively. According to the theoretical analysis formula
_{opt}_{1} = 38.83° in experiment 1 can be calculated, and αopt2=36.75° in experiment 2. This is in good agreement with the experimental results, which proves the correctness of the optimal jet angle formula.

This is basically in line with the experimental results. At the same time, the experiment also proves that the results of theoretical calculation and analysis have a certain guiding effect on the shot put. The coach can guide the athletes to master the best shot angle based on the theoretical calculation results and by measuring the athlete's shot height and initial speed.

#### Test data 2

Experiment 1 | Exit angle α/(°) | 25 | 35 | 38 | 40 | 45 | 50 |

Outgoing distance s/m | 2.324 | 2.437 | 2.5 | 2.36 | 2.726 | 2.23 | |

Experiment 2 | Exit angle α/(°) | 20 | 30 | 35 | 40 | 45 | |

Outgoing distance s/m | 1.77 | 1.815 | 1.82 | 1.754 | 1.73 |

#### Test data 1

Experiment number | Height from liquid level to outlet h′/m | Ejection height h/m | Exit velocity v0/(m·s^{−1}) |
---|---|---|---|

Experiment 1 | 1.473 | 0.8 | 5.373 |

Experiment 2 | 1.008 | 0.8 | 4.445 |

^{λ} D^{μ} Control. Journal of Advances in Computer Engineering and Technology., 2019 5(1): 1–10^{λ} D^{μ} Control

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