异步电机转子加速过程模拟

Overview

A short animation illustrating the acceleration of an asynchronous motor rotor under a rotating magnetic field. Viewers see the magnetic field lines rotate, the square loop (rotor) accelerate from rest to a steady angular speed, and key formulas appear to explain the induced emf and torque.

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Phases

#	Phase Name	Duration	Description
1	Intro	~2s	Set up coordinate axes, draw the reference circle, place the red square loop, and show the four radial magnetic field arrows. The arrows begin rotating clockwise at the prescribed angular velocity while the loop remains stationary.
2	Acceleration	~6s	The square loop starts to rotate, its angular velocity follows $\omega(t)=\omega_1\bigl(1-e^{-kt}\bigr)$. A small graph in the upper‑right corner plots $\omega(t)$ in real time. The magnetic field continues its constant‑speed rotation.
3	Steady State	~2s	The loop reaches the steady angular speed $\omega_1 = 0.8\,\omega_0$. The rotation rates of field and loop become constant, and the difference $\omega_0-\omega$ is highlighted.
4	Outro	~0.5s	Fade out the geometry while keeping the three formula boxes on screen for a brief moment, then fade everything to black.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │
│   (Title – optional, fades in with Intro)   │
├───────────────────────┬─────────────────────┤
│                       │                     │
│      MAIN AREA        │   RIGHT AREA        │
│  (Axes, circle,      │  Formulas & graph   │
│   square loop,       │  – top‑right: ω(t)  │
│   rotating B‑field)  │  – mid‑right: emf,   │
│                       │    torque           │
├───────────────────────┴─────────────────────┤
│                 BOTTOM AREA                │
│   Small caption or source note (optional) │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Optional title “Asynchronous Motor Rotor Acceleration”	Fades in at start of Intro, fades out in Outro
Main	Coordinate axes, blue dashed circle (radius 0.5), red semi‑transparent square loop $abcd$ with white vertex markers, four black radial arrows representing the magnetic field	Primary visual focus. The arrows rotate continuously at $\omega_0 = 2\pi$ rad/s.
Right	Three formula boxes (green emf, orange torque, blue steady‑state condition) stacked vertically; a small line‑graph of $\omega(t)$ in the upper‑right corner	Boxes have a white semi‑transparent background. The graph updates live during the Acceleration phase.
Bottom	Small caption such as “Parameters: $l=1$, $B=1$ T, $\tau=2$ s”	Appears after 8 s, fades out with Outro

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Notes

• Colors: Square loop – red #FF4444 with 0.5 opacity; circle – blue dashed #4488FF; magnetic arrows – solid black; formulas – colored text (green, orange, blue) on a white semi‑transparent rectangle.
• Camera: Fixed top‑down orthographic view; no camera movement.
• Timing: Total runtime ≈ 10 s at 30 fps (fits the user’s frame‑rate request). All phase durations sum to the total.
• Transitions: Simple fade‑in/out for the title and caption; linear motion for rotating elements; the angular‑velocity graph uses a linear update matching the underlying $\omega(t)$ function.
• Implementation hint: Use a single Scene class. Create the magnetic field as a VGroup of four Arrow objects, apply a Rotate animation with rate_func=linear. Update the square loop with a custom updater that computes $\omega(t)$ each frame.
• Formula placement: Each formula resides in its own MathTex inside a RoundedRectangle background to satisfy the “white background semi‑transparent box” requirement.
• No extra text: Apart from the formulas and minimal axis labels, the animation relies on visual motion to convey the physics.