MMB Chapter 17 A Top-Level Conversation with Newton
Chapter 17 A Top-Level Conversation with Newton
Li Hongde was certainly aware of this competition.
This is the first edition, spearheaded by the Provincial Department of Education, clearly aiming to make it a benchmark Class A competition.
The 5,000 yuan jackpot alone is enough to attract top students from all universities in the province to compete fiercely for it.
He even heard rumors that some schools, in order to get off to a good start, were already having teachers consider having students use existing patents to participate in competitions.
He had originally considered having Zhou Mingyuan and the others test the waters.
However, the provincial projects at hand were too tight, and manpower was insufficient, so this matter was temporarily shelved.
As a result, Zhou Mingyuan and his classmates didn't go, but Lu Feng, a freshman, signed up on his own.
"Senior Sun Hao mentioned it to me, and coincidentally, our counselor also sent out a notice, so I thought I'd give it a try," Lu Feng explained. "Since I'm participating, I should at least bring something decent to the table."
Li Hongde placed the teacup back on the table with a soft "tap".
"You dare to dream of winning an award." He leaned back in his chair, his hands clasped in front of him. "Do you know how fierce the competition is this time? All the top players in the province will participate, and some shameless old men will probably bring their star pupils. It'll be a battle of gods."
He scrutinized Lu Feng and continued, "You have talent, I don't deny that. But theory is theory, and action is action."
This is a very direct and realistic statement.
Lu Feng smiled inwardly.
Hands-on?
In his previous life, he worked in a factory for more than a decade, dealing with all kinds of machine tools and parts, from drawing, programming, processing to assembly and debugging, he experienced the entire process.
In terms of practical skills, he is confident that he is second to none.
"Just you wait and see, teacher." Lu Feng didn't argue much, but simply said calmly, "I'll definitely bring you an award."
Looking at his confident expression, Li Hongde was momentarily speechless.
This kid has a strange kind of confidence that makes people unconsciously want to believe him a little.
"Okay, it's good to have confidence." Li Hongde was eventually moved by his spirit.
He opened the bottom drawer of his desk, rummaged through it for a while, pulled out a set of keys, and tossed them to Lu Feng.
"Here's the key to the lab next door. Take it. You can come anytime you want to use the equipment there."
The key flew through the air in an arc before being caught steadily by Lu Feng.
Li Hongde added, "Can you manage on your own? You must be careful."
"It's alright, teacher." Lu Feng put the keys in his pocket. "I can manage on my own."
Looking at his overbearing manner, Li Hongde felt a little uneasy again.
Is this kid really confident, or is he just a fearless newborn calf?
Never mind, let him be.
Lu Feng didn't stay in the office any longer. He took the key and went straight back to Laboratory 302.
Zhou Mingyuan and the others had not returned yet; the entire laboratory was empty.
He walked to the materials cabinet in the corner and took out several standard-sized boards and some connectors.
Then, he walked to the small three-axis CNC milling machine in the laboratory.
Power on, calibrate, and import the 3D model of the parts that he had drawn overnight.
Next came programming.
Instead of using graphical CAM software, Lu Feng directly typed G-code on the control panel.
His fingers danced across the keys, and lines of code appeared rapidly on the screen.
M03 S2000; Spindle forward rotation, speed 2000.
G00 X10 Y15 Z5; Fast positioning.
G01 Z-2 F100; Z-axis downcut, feed rate 100.
G02 X20 Y25 I5 J0; Clockwise circular interpolation.
Every coordinate and every feed rate precisely corresponds to a contour line and a chamfer on the part.
When the last program segment was entered, he pressed the start button.
The spindle began to rotate at high speed, emitting a buzzing sound.
Coolant gushed out and poured onto the aluminum alloy sheet. The milling cutter cut in precisely, and silvery-white metal shavings splashed out with the cutting fluid.
The morning passed quietly amidst the monotonous yet rhythmic cutting sounds.
When Lu Feng turned off the machine tool and removed the last part, all the basic components of an exoskeleton arm were neatly arranged on the tray beside his table.
Mounting base for arm guard, wrist support, joint connecting block, and assist spring.
Every part is exactly the same size, with smooth edges and uniform chamfers.
Lu Feng wiped his hands and glanced at the clock on the wall; it was exactly 11:30.
He packed his things, locked the lab door, and headed towards the cafeteria.
On the way, he wasn't thinking about the exoskeleton anymore, but about that new cutting-edge technology blueprint.
Multi-scale perturbation solution for nonlinear structural dynamics
This drawing is an order of magnitude more difficult than the previous fractional calculus drawing.
The first part, in particular, concerning the general framework for multiscale expansions, involves a large number of matrix operations and complex partial differential equation transformations.
"This kind of problem, which intersects pure mechanics and mathematics, is perfect to ask Mr. Newton."
Lu Feng silently recited it in his mind.
External chat mode is now enabled.
A familiar dialog box popped up.
[Lu Feng: Sir, are you there? I have a question about nonlinear dynamics that I'd like to discuss with you.]
He replied almost instantly.
Isaac Newton: Yes.
Lu Feng directly sent over the core equations of the first part of the drawing in written form. It was a typical nonlinear differential equation for forced vibration, but both the excitation and damping terms contained high-order small parameters.
[Lu Feng: I want to perform a multi-scale expansion of this equation to separate the governing equations at different time scales, but conventional expansion methods fail when dealing with higher-order coupling terms.]
There was a silence on the other end for about thirty seconds.
Immediately afterwards, various formulas began to appear frantically on Lu Feng's screen.
[Isaac Newton: Introduce two time scales, T₀=t, T₁=εt, where ε is a small parameter.]
[Isaac Newton: Expand the solution y(t) as y(t) = y₀(T₀, T₁) + εy₁(T₀, T₁) + ...]
[Isaac Newton: Substitute the expansion into the original equation and combine the results by powers of ε.]
On the screen, the formula typed out by Newton and the derivation process in Lu Feng's mind collided and intertwined rapidly.
At this moment, the two people's thought processes reached an astonishing synchronization.
Lu Feng's fingers were also tapping rapidly.
[Lu Feng: The ε¹ order equation contains a secular term, making it unsolvable.]
[Isaac Newton: Introduce an undetermined function A(T₁) into the general solution of y₀, and use the secular conditions of the y₁ equation to determine the governing equation of A(T₁).]
This is precisely the core idea of the perturbation method.
But Newton suddenly stopped halfway through the derivation.
[Isaac Newton: Wait a minute, in your original equation, what is the physical meaning of this nonlinear damping term c₂ẏ³? Why use the cube of the velocity to describe damping?]
That's a very good question.
Because in Newton's time, damping was generally considered to be linear, at most taking into account quadratic air resistance.
Cubic damping is a phenomenon that was discovered later in the study of high-speed fluids and some special polymer materials.
[Lu Feng: Sir, you can understand it as a kind of... turbulence effect. When an object moves at high speed in a medium, complex vortices form behind it. The resistance of these vortices to the object is no longer a simple linear relationship, but a higher-order nonlinear effect.]
[Isaac Newton: Vortex...turbulence...]
Newton repeated the two words, and a long silence fell on the other end of the chat box.
Lu Feng knew that the seed of knowledge had already been planted in his heart.
A full minute passed before Newton's message popped up again, but the content was completely different from before.
[Isaac Newton: I understand. According to your turbulence model, the nonsecular condition of the y₁ equation needs modification. The governing equation for A(T₁) should be an ordinary differential equation containing a cubic nonlinear term.]
Lu Feng immediately followed his train of thought.
[Lu Feng: Yes, this equation can be solved using the Jacobian elliptic function.]
[Isaac Newton: That's right!]
Two geniuses, separated by more than three hundred years, clashed intensely at this moment, launching a joint attack on a complex mathematical problem.
On the screen, lines of derivation process appeared one after another, and finally a concise and elegant analytical solution appeared at the end of the dialog box.
The first part of the blueprint has been solved.