[2022 Jiangxi graduate mathematical modeling] curling movement idea analysis and code implementation

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2022 year 7 month 4 Number 10：49

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2022 year 2 month 4 solstice 20 China successfully hosted the Beijing Winter Olympic Games on August , Beijing has become the first city in the world to host both the Summer Olympics , Also held the Winter Olympic Games “ The city of double Olympics ”. The Beijing Winter Olympics has set up 7 Big item ,15 Items ,109 A small item , Among them, curling is fun , Ornamental , Technology and collaboration have become a popular and concerned project . Curling is a throwing sport on ice , It originated in the 14 Scotland in the th century ,1924 As a performance item, it was included in the first winter Olympics ,1998 It was listed as the official event of the Winter Olympics .

    Curling consists of a body 、 It is composed of handle and bolt , The circumference is about 91.44 centimeter , The height is about 11.43 centimeter , The quality is about 19.96 kg . The standard venue of the competition is long 44.5 rice , wide 4.32 rice , One end is home base , The picture has a diameter of 1.83 The circle of meters serves as the player's tee ; At the other end is camp , from 4 The diameters are 0.15 rice 、0.61 rice 、1.22 Rice and 1.83 The concentric circles of meters . There is a solid blue line at both ends of the site , They are respectively called the avantgarde line and the defender line . After the curler is thrown , If you don't pass the front line or exceed the back line, it will be regarded as invalid , Will be cleared off the court .

    Two teams participate in each game , Factions 4 Players play , Divide into first base 、 second base 、 third base 、 Fourth base , Cross throw the pots in order , Every game 16 Pot , Together with 10 game . When a team member throws a pot , The two companions of our team can quickly wipe the ice with ice brushes in front of the curling slide , To control the direction and speed of curling . While trying to slide the curler to the center of the circle , You can also use curling to knock the other side's curling out of the camp or your own curling on the field into the center of the camp . After the curler crosses the center line , Only one member of both sides can brush the ice for his curling bottle , And only the master can brush the ice for each other's curling , To destroy the opponent's tactics .

Please build a mathematical model , Complete the following tasks ：

   problem 1   Without brushing ice , What strategies are adopted , Achieve the following goals ：

 (1)  When there is no curling in the camp , Make the curler stop in the camp .

 (2)  When there is an opponent's curler in the camp , Knock the opponent's curler out of the camp , And my curler stopped in the camp .

 (3)  When there is an opponent's curler in the camp , Knock the opponent's curler out of the camp , At the same time, his curling out of the camp together .

 (4)  When there are two opposing curlers in the camp , Knock both curlers out of the camp , And I stopped in the camp .

 (5)  When there is an opponent's curling in the camp , There is also your own curling , Knock the opponent's curler out of the camp , And his curling remains in the camp .

  problem 2   Consider ice brushing , Question answering 1 Several problems in .

  problem 3   If there is curling in front of the camp , Re study the problem 1 And questions 2.

2 Parsing and code implementation

Ideas complete link ：https://mianbaoduo.com/o/bread/YpyWlp9v
Mechanical analysis of curling , Including direct contact 、 Side impact 、 Straight line motion 、 Curvilinear motion 、 Friction does not change 、 Friction is variable .
（1） Invest in technology
Concept ： Pitching refers to the effective pitching of athletes into the base camp area . Throwing technology is the most basic throwing technology , It belongs to steamed bread pot technology . The throwing technology requires that the target pot be put into the predetermined effective scoring area , Form an effective score , What it wants to achieve The requirements of the arrived tactical purpose are low , This technology usually appears in the pot throwing application of the first player in each game . The pitcher is using When investing in technology , Generally, there is no need to make too powerful rotation , The strength of throwing the pot is relatively moderate , Pitchers use pitching skills The success rate during operation is high , Generally, there is no need for ice brushing team members to make a substantial route adjustment to the throwing pot .
Mechanical analysis ： A little

（2） Hitting technique

Concept ： Hitting refers to an athlete throwing a pot hard to hit the scoring pot of the other party in the base camp , And leave the hitting pot behind Hit away the effective throwing pot at the pot position . Hitting is a typical fast pot technique , The purpose of hitting is to hit the target pot , And cast The throwing pot stays at the position of the beaten pot , Its tactical purpose is , Strike away the opponent's scoring pot and form an effective score . complete The hitting technique requires the pitcher to throw the pot at the beginning , Increase the pedal strength of the back swing and floating legs , Give the pot a big forward momentum ; Deliberately control the rotation angle of the curler when taking the shot , Reduce the collision angle between the throwing pot and the target pot , Try to cast The throwing pot collides with the target pot head-on . At the same time, the ice brushing team needs to know the forward route of the throwing pot and the target pot after the two pots collide Carefully observe the running route , Take positive adjustment actions , Help the throwing pot hit the target pot accurately , Make target The pot was knocked out of the base camp faster , So as to achieve the predetermined tactical purpose , Improve the success rate of pot throwing .

Mechanical analysis : A little

（3） Empty Technology

Concept ： Emptying refers to the athlete throwing a pot hard to hit the opponent's target pot in the base camp , At the same time, the ball thrown by your side The pot is also out of the effective throw pot . The use of emptying technology is mostly used to clear the opponent's scoring pots in the camp at a fixed point , Has reached minus Score less , The purpose of ensuring the smoothness of the pot throwing route . Because when using emptying Technology , Need to hit the ball The pot collided with the target pot and was out successively , Then ask the pitcher to throw the pot at the beginning , Increase the pedaling force of the back swing and floating legs degree , Give the pot a greater forward impulse ; Deliberately increase the rotation angle of the curler when taking the shot , Increase the throwing pot and the target pot Collision angle . When hitting the pot , Try to adopt the collision mode of side large angle collision . The ice brushing team will throw Carefully observe the forward route of the pot and the running route of the target pot after the collision of the two pots , Take positive adjustment actions , help Help the throwing pot hit the target pot accurately , Make the target pot and throwing pot out successfully , To achieve tactical objectives .

Mechanical analysis ： A little

（4） Double click Technology

Concept ： Double click refers to an athlete throwing a pot hard to knock out two or more pots in the opponent's base camp , And hit the ball The effective throwing of pots that can remain in the base camp . Double click technology is a kind of fast pot technology , Double click to set two or two Above the target ball , The throwing pot is required to hit and hit the first target pot , With the help of the reaction of collision with the first target pot Rotation caused by force and collision , Continue to hit one or more target pots , And hit it out of the effective scoring area , from And achieve the effect of hitting multiple opponent's target pots . In order to achieve the tactical purpose of hitting multiple target pots , Double click technical requirements According to the situation on the court, the pitcher should give the pitcher a large enough release speed and a large rotation , And according to Liang Mu Mark the position between the pots , Accurately calculate the release angle ; Due to the linear speed and rotation of curling in operation The linear speed is fast , The ice brushing team needs to follow the throwing pot , According to the ice condition in front of the curling operation and the target curling is hit after , The ice surface of its operation route shall be brushed and adjusted .

Mechanical analysis ： A little

（5） Passing skill

Concept ： Passing refers to an athlete throwing a pot hard to hit , Pass by hitting the opponent or your own target pot , Take each other The pot blows , An effective throwing pot that hits its own pot to a more favorable position . Passing is to use multiple pots to hit and collide continuously , A technique that enables the collision force to be continuously transmitted between multiple pots , Its purpose is to transmit the force of multiple targets through continuous transmission Hit the favorable position of cranium . This requires athletes to throw the pot , Not only should we consider the hitting pot and the hit target pot The position of the strike , And also pay attention to the collision position between the beaten pot and the next target pot after being knocked out ; It also puts forward higher requirements for athletes' pitches , We need to do more in the control of release force and rotation angle force II Exquisite ; While the ice brushing athlete adjusts the trajectory of the throwing pot before the collision , Also note that after a series of After the collision , Adjust the running track of the target pot after collision , Achieve the predetermined tactical goal .

Mechanical analysis ： A little

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