Regarding the three-dimensional function trajectory correction problem sent by Liu Rongxing, Wang Hao already had a "vague" conclusion in his mind.
The conclusion is two words-'feasible'.
The reason why he said "feasible" is a vague conclusion is because he is not 100% sure, but the probability of certainty is more than 90%.
If you want to be completely sure, you have to come up with a plan.
Wang Hao is not in a hurry to give an answer. Mathematics is very rigorous. There is no such thing as "probably feasible". What is feasible is feasible, and what is not feasible is not feasible. A definite answer must be given.
He also hopes to do a more perfect job rather than give ambiguous answers, especially when the question may involve the trajectory of ballistic missiles.
This kind of research must be carried out with caution and caution.
In addition, it was impossible for him to give up halfway through the research.
Although the inspiration value was still only 60 points, he felt that he was very close to completion.
The difficulty in trajectory correction of three-dimensional functions is actually calculation. How to orient one function to the trajectory of another function is very important. Numerical calculations are very important, and the similarity needs to be very precise.
For example, a simple function x=1.
If the modified function is x=2, the difference is too large, and the approximated function x value must be limited to the value '1'.
Precise calculations related to functions are very important, and at the same time involve the calculation of complex equations. It is even said that equation calculation is the core, because the calculation of functions will eventually become the calculation of equations.
This problem involves external forces, or forces that impact rapidly in a short period of time, or forces that are continuous, and it must involve complex equations.
The calculation of complex equations is the biggest difficulty in calculation problems.
Among a series of complex equations, the most difficult one is the partial differential equation, the NS equation. In fact, the NS equation is the fluid mechanics explanation of Newton's second law.
So the problem ultimately comes to the study of complex equations.
Wang Hao's research is not in a hurry. He will think about it for a while, and if he can't think of anything, he will look at other content.
Teaching every day is a must-do homework, and teaching can slowly accumulate inspiration points.
The current teaching has moved beyond function theory and entered the stage of computational mathematics. Of course, it is impossible for him to explain function theory in half a month. He only explained some main content and did not continue to involve advanced knowledge.
The scope of computational mathematics is too great.
This subject is related to differential equations, vector analysis, matrices, Fourier transforms, complex variable analysis, numerical methods, probability theory, mathematical statistics, operations research, control theory, combinatorial mathematics, information theory and many other branches of mathematics. It is also
Includes the study of mathematical problems posed from a variety of application areas.
Therefore computational mathematics can be regarded as a part of applied mathematics.
The first thing Wang Hao talked about was the problem of algebraic equations. Algebraic equations are very prominent and the most involved problems in computational mathematics.
His small class has been open for about half a month. At first, many doctors and even professors came to attend the class, but gradually some people stopped coming.
For example, the professors and associate professors upstairs.
Because the content Wang Hao talks about is not in-depth, it is basically some basics. It can be helpful for doctoral students and graduate students to deepen their understanding of knowledge in the field of mathematics, but it is difficult for professors to gain anything. At most, they can only re-learn
Reviewing it again does not have much practical significance.
So the number of people in the class has stabilized, with about twenty people coming each time.
Wang Hao was still very satisfied with the number of people. Twenty people were enough. He continued his lecture rhythm, "In the field of algebraic equations, we generally recognize the fact that there is no root finding formula for algebraic equations of the fifth degree and above.
.”
"Therefore, only approximate solutions can generally be obtained for this type of algebraic equations, and the method of obtaining approximate solutions is the method of numerical analysis."
He put down the book in his hand and continued, "For this type of complex equations, our research direction is mainly to find approximate solutions to individual types of equations through analysis."
This is a small research direction.
Just like the thesis of some doctoral students and graduate students, including the solution of many partial differential equations, the solution of complex algebraic equations is also a large research direction, but it is difficult to produce great results.
Wang Hao continued, "But in practical applications, the solution method of substituting numerical values ​​is more direct."
Helen suddenly raised her hand and asked, "Teacher Wang, for some equations, would it be much simpler and more direct to obtain approximate solutions by substituting numerical values ​​than through mathematical analysis?"
"Moreover, even if numerical analysis is used to solve the problem, the approximation is not necessarily closer than the numerical solution and the exact solution, right?"
Wang Haodao, "In some cases, this is indeed the case, but in other cases, the numerical solution will be very complicated."
He nodded and said, "Helen's question is very good. Which method is more suitable, numerical solution or analytical solution, depends on the complexity of the equation."
"If it is an equation that has no clue at all, it will be difficult to find the approximate direction using numerical solutions."
"The equation is relatively simple, and it will be easy to solve it by inserting numerical values ​​into it."
As he was talking, he suddenly thought of the research problem, and an idea suddenly flashed in his mind, and at the same time, the system was refreshed with new information.
[Task three, inspiration value 11.]
"It makes sense!"
Wang Hao suddenly felt a sudden realization. He glanced at Helen appreciatively and continued with the rest of the course.
After the explanation was completed, he returned to the office and began to do research seriously.
I encountered computational problems in my previous research. Because I am very good at mathematical analysis, I felt that I had reached a dead end and kept doing research in the direction of mathematical analysis.
However, mathematical analysis is relatively too complex, and the analysis process is unlikely to be applied by computers.
This complexity makes the problem impossible to solve.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! He has been troubled by this.
Helen's question reminded him that it was not necessary to follow the path of mathematical analysis. It was relatively simpler to directly bring in the numerical values.
…
137.
This is a confidential scientific research institution specializing in ballistic research.
The two-story building surrounded by mountains and forests is the main research and development base of Institute 137. The sunlight shines into the conference room from the window, reflecting the faces of the people who are arguing.
A young man in his thirties put his hands on the table and said forcefully, "Qian Xuesen's ballistics also has limitations!"
"Our research on maneuverable gliding technology cannot be limited to Qian Xuesen's ballistic trajectory, but must also develop in other directions."
Another middle-aged man in his forties replied, "What you say is very interesting. The trajectory of motorized gliding technology was originally proposed by Mr. Qian Xuesen. What other directions can be developed? Do you have the ability to tell me?
?”
The young man immediately replied, "I can't tell you now, but do you admit that Qian Xuesen's ballistic trajectory has limitations? It is difficult for conventional missiles to maintain that trajectory until it hits the target."
"In addition, there are also studies in other countries. Qian Xuesen's ballistics is public information. It was proposed by Mr. Qian Xuesen when he was studying abroad in Amerikan. Their information may be no less than ours."
"As long as they can understand this technology thoroughly, they can use computers to lock the route for anti-missile purposes."
"What we are studying now is how to avoid being anti-missile. No matter how beautiful the trajectory of the missile is, what's the use? Before hitting the target, we still have to rush directly towards it."
"Now the only way to ensure hitting the target is hypersonic speed, which can accelerate to Mach 10 or Mach 20, but that technology cannot be widely used."
The middle-aged man immediately retorted, "You said to develop new technology, just develop new technology. How can it be that simple? Now we don't even know the direction. And we are already leading in Qian Xuesen's ballistic trajectory."
"How do you know you are in the lead? Who can determine the lead? Have you verified it?"
"Why am I not sure?"
"You can't be sure."
"..."
The two people slapped the table and shouted at each other, almost starting to use their hands.
The door of the conference room.
Zheng Guofeng couldn't help but smile bitterly after hearing this. Similar arguments occurred in every meeting. They were now discussing the direction of future research and development.
this is very important.
Although Qian Xuesen ballistics technology has been mastered, no technology can be perfect, and Qian Xuesen ballistics also has its limitations.
Qian Xuesen's ballistics refers to maneuvering gliding technology, which can be understood as allowing ballistic missiles to change directions like cruise missiles, and the trajectory will become very uncertain.
However, the use of similar technologies will definitely take up a certain amount of weight, and not every missile can be used.
Domestic missile development has achieved overtaking in a corner to a certain extent.
They developed directly from conventional ballistic missiles to maneuvering gliding technology, directly skipping the stage of re-entering maneuvering gliding ballistic missiles.
To be continued...