sbdcsierra Chapter 60 The All-Powerful Lu Feng, and the Unsettled Competition Manager
Chapter 60 The All-Powerful Lu Feng, and the Unsettled Competition Manager
At 10:03, Lu Feng had already started writing on the draft paper.
The first question is about the optimal transfer trajectory under the gravitational slingshot effect.
He first drew a simplified heliocentric coordinate system, and the relative positions of the three points, Earth, the target planet, and the Sun, were marked by trigonometric relationships.
Then list the basic system of equations for the Lambert problem next to it.
Given the position vectors of the starting and ending points, and the flight time, solve for the semi-major axis and eccentricity of the elliptical transfer orbit.
The pen moved very fast, but the spacing between each symbol was perfectly controlled.
Riemann's focus came into play at this moment.
The sounds of keyboards clattering around me, the rustling of pages turning in the next room, and the hissing of the air conditioner vents were all automatically filtered out as background white noise.
Zhou Xiaoxiao moved a chair to Lu Feng's left and sat down without saying a word, just staring at the tip of his pen.
After Lu Feng finished writing the standard form of the Lambert equation, he looked up at her.
"Please help me calculate the numerical root of this transcendental equation using Newton's method of iteration, with π as the initial value."
Zhou Xiaoxiao took the draft paper and started calculating with her head down.
Lu Feng didn't wait for her answer; he flipped directly to the second draft paper and began to work out the second question.
Rocket landing dynamics modeling.
This is the real highlight of the whole question.
He drew a simple side view of the rocket on a piece of paper.
It features a conical fairing, a cylindrical body, four landing legs at the bottom, and a central variable-thrust main engine.
The diagram is small, but the annotations of the key parts are extremely precise.
The thrust vector angle δ, aerodynamic angle of attack α, the position of the rocket's center of mass, and the hinge point of the landing legs are all marked with arrows and symbols at their corresponding positions.
Chen Jing peeked over from the side, saw the simple line drawing, and paused for a moment.
"You can draw this too?"
"I saw it online," Lu Feng said casually.
Chen Jing didn't understand, but she didn't ask any further questions.
Her task was to assist in deriving the aerodynamic equations, so she took the simplified diagram with the parameters marked on it from Lu Feng and began to list the drag formulas next to it.
11:45.
One and a half hours.
Seven sheets of draft paper filled with formulas were already stacked in front of Lu Feng.
The complete mathematical model for the first question includes a multi-segment Lambert transfer orbit optimization model with gravity-assisted velocity increments. The objective function is the total flight time, and the constraints include the upper limit of fuel mass and the planetary window period.
The solution method uses sequential quadratic programming.
The complete mathematical model for the second question is a six-degree-of-freedom rocket landing dynamics equation of state, which includes four control variables: variable thrust, thrust vector angle, aerodynamic drag, and landing leg deployment timing.
By using the Pontryagin maximum principle to establish the adjoint equation, the optimal control problem is transformed into a two-point boundary value problem.
Zhou Xiaoxiao handed over the calculated numerical roots. Lu Feng glanced at them, nodded, and directly substituted them into the orbital parameters from the first question.
"The modeling part is basically finished." Lu Feng put down his pen and stretched his wrists.
Chen Jing stared, her mouth agape, her gaze sweeping back and forth across the seven draft papers three times.
All morning.
While other teams were still arguing over the choice of coordinate system for the first question, they had already finished modeling both questions.
"Junior, you're not human." Chen Jing uttered her first exclamation of the day from the bottom of her heart.
Lu Feng didn't respond to that, and turned to look at the programming team.
"Senior Li Hao, the modeling results are here. You can start writing the code now."
He handed over seven sheets of draft paper. Li Hao took them and, together with Wang Zhe and Liu Yu, studied them for about three minutes.
The expressions on the three people's faces grew increasingly serious.
It's not that they couldn't understand it; quite the opposite, they understood it completely.
It was only after understanding it that I realized how difficult it was to implement this model in code.
Numerical integration of the six-degree-of-freedom state equations requires writing a fourth-order Runge-Kutta solver.
Solving the adjoint equation of Pontryagin's maximum principle requires iterative solutions to two-point boundary value problems using the shooting method. While optimizers for sequential quadratic programming can utilize readily available libraries, the Jacobian matrix of the constraints must be manually derived and hard-coded into the code.
"This...the workload is a bit heavy," Li Hao said cautiously.
Wang Zhe was even more direct: "Boss, I estimate this amount of code will take until tomorrow afternoon to write."
Lu Feng glanced at the clock on the wall.
Ten past twelve.
More than two hours have already passed out of the total 72-hour time limit.
If the programming phase drags on until tomorrow afternoon, the time left for writing the paper and validating the model will be too short.
He thought for two seconds.
"I'll write it."
Li Hao was taken aback.
"The three of you will be responsible for testing and debugging, while I will build the main program framework."
After Lu Feng finished speaking, without waiting for their reaction, he pulled out the chair next to his computer and sat down.
Open your Python IDE and create a new project file.
Fingers landed on the keyboard.
"Tap tap tap tap—"
That familiar, dense, almost continuous tapping sound rang out again.
Li Hao stood behind Lu Feng, his hands hanging at his sides.
He watched the code on the screen scroll down at an unreal speed.
No comments are provided, and no comments are needed.
Because the code itself is a comment.
Each variable name strictly corresponds to the mathematical symbols on the scratch paper, and the input and output of each function are clearly visible.
Wang Zhe stood next to Li Hao, craning his neck.
He wanted to help, but couldn't find a starting point.
Liu Yu silently poured Lu Feng a glass of water and placed it on the right side of the keyboard.
Lu Feng didn't even look up. He reached for the cup with his left hand, took a sip, put it down, and continued tapping.
1:30 PM.
Chen Jing went to the cafeteria and brought back six boxed meals and a bag of bottled water.
"Dinner's ready, dinner's ready."
Zhou Xiaoxiao and the three members of the programming team took the boxed lunches and started eating.
Lu Feng's boxed lunch was placed on the corner of the table. He glanced at it but didn't stop eating.
3:20 PM.
Lu Feng pressed the run button.
On the screen, the trajectory optimization program for the first question begins its iterative iteration.
After about forty seconds, the progress bar displayed a set of orbital parameters and a 3D projection map of the transfer orbit within the solar system.
The blue curve starts from Earth, passes Venus, gains velocity using a gravitational slingshot, and circles halfway around the sun along an elegant elliptical arc before returning to Earth.
Total flight time: 487 days.
Fuel consumption: within the constraints.
Immediately afterwards, the landing simulation program for the second question also finished running.
An animation appeared on the screen showing a simplified rocket model decelerating from an altitude of 2,000 meters. The thrust vector was adjusted in real time according to the attitude. The landing legs extended at a height of 50 meters above the ground, and finally the rocket landed steadily at a speed of 1.2 meters per second.
The bottom output shows the time history curves of the optimal fuel consumption and each control variable.
Li Hao stared at the landing animation for a full ten seconds, then slowly turned his head to look at his computer, which hadn't been used at all since it was turned on.
Let's just shut it down.
He swallowed hard and asked, "Junior, what exactly are you keeping the three of us around for?"
"Run a parameter sensitivity analysis for me later, and check the robustness of the model by changing a few sets of initial conditions."
Li Hao nodded, finally finding his own value.
Although this job can be done by one person in half an hour.
Behind the computer room.
Wu Heming didn't know when he had walked to the side and rear of area A-07.
He crossed his arms and looked at Lu Feng's screen through the gap in the partition.
He has been involved in judging and organizing mathematical modeling competitions for over twenty years and has seen many exceptionally talented students.
He had seen people with outstanding modeling skills.
He had also seen people with astonishing programming speeds.
But I've never seen anyone do both of these things to such an extent.
He turned his head and glanced at the three boys in the programming group in area A-07.
The winners of the provincial programming competition were sitting in a row next to him, holding boxed lunches, looking at Lu Feng's back with blank expressions.
Like three temporary workers whose jobs were taken away.
Wu Heming withdrew his gaze, walked back to his corner, took out his phone from his pocket, opened his contacts, and found a name.
Chairman of the Provincial Mathematical Society.
He hesitated for two seconds, then put the phone back in.
Let's wait until the final paper is out before making any decisions.
What if the paper turns out to be a complete mess?
After completing the modeling and programming, Lu Feng leaned back in his chair, unscrewed the bottle of mineral water that Liu Yu had placed on the corner of the table, and took two gulps.
Chen Jing had already opened Word, her fingers hovering over the keyboard.
"The rest of the paper is up to me." She gave Lu Feng an OK sign. "Just give me a framework, and I'll write the rest."
Lu Feng took a piece of paper from the side, spent two minutes listing the chapter framework of the paper and the core arguments of each section, and handed it to her.
Chen Jing took it, read it once, and nodded.
"Understood, go and rest for a while."
Lu Feng then realized that his neck was so sore it felt like it was about to break.
He stood up, stretched his shoulders, and walked to the window.
The sky outside the window was already getting dark.