dkrc Chapter 59 of the competition begins; this question is about space exploration, right?
Chapter 59 of the competition begins; this question is about space exploration, right?
At 7:45 a.m., in the lobby on the first floor of the computer center.
When Lu Feng pushed the door open, his first reaction wasn't to look for his teammates, but to glance at the doorway.
Two middle-aged men in dark suits stood next to the registration desk, wearing blue badges with white lettering that read "Provincial College Student Mathematical Modeling Competition Organizing Committee." Behind them stood three other people, one with a DSLR camera around his neck, and the other two each holding a stack of folders, checking the network configuration of the computer room with the computer center's administrator.
On the registration desk, there was a row of bottled water and several unopened boxes of ballpoint pens. Next to it stood a KT board with the full name of the competition and the organizer printed on it.
Provincial Department of Education. Provincial Mathematical Society. Provincial Association for Science and Technology.
The three stamps were stamped neatly.
Lu Feng sighed silently to himself.
The scale of the operation was larger than he had anticipated.
This provincial-level Class A competition is no joke; there were so many on-site supervisors alone, so it seems the subsequent marking and defense stages will only be more rigorous.
"Junior!"
Chen Jing's voice came from the right side of the hall. She stood beside a pillar, clutching a transparent file folder containing a leave slip and her student ID. Zhou Xiaoxiao was next to her, looking down at something on her phone.
The three members of the programming team also arrived. Li Hao leaned against the wall, resting with his eyes closed, while Wang Zhe and Liu Yu squatted on the ground, each holding a laptop, seemingly checking the software environment.
Six people, all here.
Lu Feng walked towards them and nodded.
"Everyone's here so early?"
"How could I sleep?" Chen Jing's voice was tight, and her eyelids kept twitching as she spoke. "I woke up at four o'clock, tossed and turned until five-thirty, and then I just got up and washed my hair."
Zhou Xiaoxiao raised her face, her dark circles making it look like she was wearing smoky makeup.
"I had a nightmare last night. I dreamt that after the exam started, all the questions were written in German, and I couldn't understand a single word."
Lu Feng's lips twitched slightly as he looked at the two of them, who seemed to be facing a formidable enemy.
"Don't worry, it won't be in German."
"What if it's in French?" Zhou Xiaoxiao asked tentatively.
"Then there's even less to worry about. Half of the French mathematical papers are nonsense."
Chen Jing couldn't help but chuckle. Her tense nerves relaxed a little.
At 8:20, the organizing committee staff began guiding the participating teams into their designated computer rooms.
Room 301 has been rearranged. The originally open seating area has been divided into several independent areas by partitions, each equipped with three networked computers and a printer.
Team numbers were labeled on the tables, and a case of bottled water and a pack of A4 paper were placed next to each table.
The room number for Hong Kong City University is A-07, and it's located by the window.
Lu Feng led the five men to area A-07 and sat down. Li Hao, Wang Zhe, and Lu Feng used the three computers respectively, while Liu Yu brought his own laptop as a backup.
Chen Jing and Zhou Xiaoxiao were at the innermost side, with draft paper and reference books laid out in front of them.
The team from the Provincial University of Science and Technology, consisting of four men and one woman, sat in seat A-06 next door, all with solemn expressions.
One of the boys wearing round-framed glasses recognized Lu Feng, nudged his teammate's arm, and muttered a few words.
The teammate turned his head and glanced at him, a complex look flashing in his eyes.
Clearly, Lufeng's performance in the Mechanical Innovation Competition has spread throughout the university community across the province.
The news that a freshman who can handcraft an exoskeleton is competing in mathematical modeling is enough to keep his opponents up at night.
9:45.
The projection screen at the front of the computer room lit up. A man around fifty years old with gray hair walked to the front of the stage, holding a microphone.
"Dear participating students, I am Wu Heming, the on-site supervisor of this competition and the vice chairman of the Provincial Mathematical Society."
He surveyed the server room, his voice low but commanding.
"As you all already know the competition rules, I'd like to emphasize three points. First, the competition questions will be released precisely at 10:00 AM. The questions will be uploaded to the official website in the form of an encrypted compressed file, and the password will be revealed on the screen at 10:01 AM. Second, you must not communicate the content of the competition questions to any external personnel within 72 hours. Third, the final submissions must include the paper PDF, the source code, and the data files; none of them can be omitted."
He put down the microphone and retreated to a corner.
9:55.
The air in the computer room became thick and sticky. The sounds of keyboard typing, page turning, and even the unscrewing of mineral water bottle caps all disappeared.
Chen Jing's hand rested on the mouse, her knuckles turning white.
Zhou Xiaoxiao twirled a pen between her fingers three times, then dropped it on the floor. When she bent down to pick it up, she almost hit her head on the corner of the table.
Li Hao closed his eyes, his chest heaving faster than usual.
Lu Feng opened his browser, entered the official website address, and the page loaded.
A gray download button is displayed in the center of the homepage, with the words "Competition Problem Download (Not Available)" on it.
10 o'clock sharp.
The button changed from gray to green.
Click to download in Lufeng.
A 28KB compressed file was downloaded in 0.3 seconds.
A line of large red text popped up on the projection screen.
Unzip password: SMCM2012APXH7
Lu Feng entered the password to unzip the file.
There is only one PDF in the folder.
He double-clicked to open it.
A4 layout, with the title in bold and black, and the body text in Song typeface, size 4.
The moment Lu Feng saw the first line of the question, his eyelids twitched.
Deep Space Probe Orbit Optimization and Reusable Launch Vehicle Landing Dynamics Modeling
The question is divided into three sub-questions.
Question 1: Establish a mathematical model to describe the optimal transfer trajectory for a probe launched from Earth, which, with the aid of planetary gravity (i.e., the gravitational slingshot effect), orbits the Sun once and returns to Earth, with the requirement of minimizing the total flight time while satisfying fuel constraints.
Question 2: For the vertical recovery and landing process of the first-stage booster of a launch vehicle, establish a complete dynamic model that includes aerodynamic drag, thrust vector control and landing leg deployment timing, and provide the optimal fuel consumption scheme.
Question 3: Based on the analysis of the first two questions, from the perspective of engineering feasibility, demonstrate whether the reuse of the first-stage booster of a launch vehicle is economically and technically feasible.
Lu Feng stared at the screen for five seconds.
Rocket recovery.
2012 years.
This question, if asked today, would practically be testing your ability to predict the future.
Because at this time in 2012, SpaceX's Falcon 9 had just completed its first commercial resupply mission, and first-stage recovery technology was still in the PowerPoint stage.
Ninety percent of aerospace engineers worldwide consider this a pipe dream.
But Lu Feng knew that three years later, the Falcon 9 would complete the first-stage landing and recovery of an orbital-class rocket in human history at Cape Canaveral.
He knew that this was not only feasible, but also bound to succeed.
"What...what the hell is this?"
Chen Jing's voice came from the side, with a noticeable tremor.
She stared at the question on her computer screen, her face ashen.
"Rocket? Gravity slingshot? Is this mathematical modeling or a doctoral dissertation defense in aerospace engineering?"
Zhou Xiaoxiao was even more straightforward; she simply lay face down on the table, holding her head in her hands.
"Oh no, oh no, oh no, I've only ever seen what a rocket looks like on TV..."
On the programming team's side, Wang Zhe and Liu Yu looked at each other in bewilderment.
Although Li Hao didn't say anything, his hand holding the mouse was visibly stiff.
The other teams in the computer room reacted in much the same way.
The boy from the neighboring university of science and technology, who wore round-framed glasses, buried his head in his arms.
An atmosphere of collective despair permeated the entire 301 computer room.
Lu Feng leaned back in his chair, his hands clasped behind his head.
His mind was already rapidly breaking down the structure of the problem.
The core of the first question is orbit optimization under a multibody gravitational field, which is essentially a variational solution to a constrained three-body problem.
The initial trajectory design can be performed using the classical solution to the Lambert problem, and then an iterative optimization can be performed by introducing a gravity-assisted velocity increment model.
The second question is more direct: modeling the landing dynamics of rocket recovery.
This is a typical optimal control problem. Using the Pontryagin maximum principle, we establish a state equation that includes the thrust vector angle and aerodynamic drag. The objective function is to minimize landing fuel consumption.
The third question is an open-ended question that requires you to combine the quantitative analysis from the first two questions and provide an economic assessment of rocket recovery.
The entire logic was clear in Lu Feng's mind in less than thirty seconds.
He turned his head and looked at Chen Jing.
"Don't panic."
The two words were pronounced in a very flat tone.
Chen Jing looked up, her eyes a little red.
Lu Feng's gaze swept over the faces of the five people, looking at them one by one.
"This problem looks intimidating, but when you break it down, the mathematical tools used in each subproblem are ones we've practiced."
He held up three fingers.
"Track optimization, using variational methods and numerical iteration. Landing control, using optimal control theory. Economic analysis, using Monte Carlo simulation and sensitivity testing."
"No module is beyond our capabilities."
As Chen Jing listened to him unravel the strips one by one, her breathing gradually calmed down.
Zhou Xiaoxiao also raised her head from the table.
"Now, let's divide the tasks." Lu Feng spoke slowly, but each word was clear and concise.
"I was responsible for the modeling framework for the first and second questions, Chen Jing assisted in deriving the aerodynamic equations for the second question, and Zhou Xiaoxiao prepared the economic analysis literature materials for the third question."
He switched to the programming group.
"Li Hao, you'll write the trajectory simulation for the first question using MATLAB. Wang Zhe and Liu Yu will be responsible for the numerical solution of the landing dynamics for the second question using Python."
Six pairs of eyes converged on him, and the confusion and fear he felt were visibly fading away.
Chen Jing took a deep breath and patted her cheeks.
"Okay." She stood up, tied her hair into a high ponytail, and then grinned at Lu Feng.
"My modeling workload was the lightest, so I took care of all the logistics. Bringing meals, water, and taking out the trash were all my responsibility."
In the corner at the back of the computer room.
Wu Heming crossed his arms and watched the movements in area A-07.
Just now, when the competition questions were distributed, he made a point of observing the reactions of several key teams.
Most teams reacted with the expected shock, followed by a long silence and bewilderment.
But the team from Hong Kong City University was different.
The young man sitting in the very middle never stood up from beginning to end.
After reading the question, he didn't even discuss it with any of his teammates. Instead, he quietly thought about it for less than a minute before completing the task assignment in a very short time.
More importantly, after he spoke, the five previously panicked team members almost simultaneously fell silent.
Wu Heming pushed up his glasses.
It seems that he is the core of the entire team.