Interactive Kinematic Simulators:
Bridging Classical Impacts & Magnetic Coupling
The interactive tools below provide a visual bridge between 350-year-old textbook collision mechanics and the non-contact dynamics of Active Magnetic Oscillation (AMO). While analytical equations can obscure the underlying mechanics, observing energy handovers in real time offers intuitive, cognitive clarity for researchers and learners alike.
For Physicists & Engineers
Jump to Tool ↓A visual sandbox to explore macro-level energy exchange, observe bifilar parallel linkages that eliminate tilt shear, and examine progressive 2.5-cycle handovers where standard Simple Harmonic Motion (SHM) fails to apply.
For STEM Students & Educators
Jump to Tool ↓An interactive laboratory to test conservation of momentum and kinetic energy, understand why Newton’s Cradle dampens so quickly in the real world, and see what happens when physical impacts are replaced by magnetic cushions.
Active Magnetic Cradle (AMC) Coupled Telemetry
Non-contact bifilar dipole carriages demonstrating progressive 2.5-cycle Active Magnetic Oscillation (AMO) energy handover.
Non-Contact Magnetic Coupling & Parallel-Face AMO
In physical Active Magnetic Cradle (AMC) systems, each horizontal dipole carriage is suspended using a dual-line bifilar linkage. This geometry ensures the repelling South–South (S–S) magnetic pole faces remain horizontal and parallel throughout the entire stroke, eliminating the vertical magnetic tilt shear that occurs with single-pivot spherical pendulums.
Compressing against a non-contact magnetic repulsion cushion, the system exchanges energy progressively rather than through instantaneous mechanical impact:
- 2.5 Cycles: The system reaches a balanced 50/50 phase equilibrium between the two carriages.
- 5.0 Cycles: Full kinetic energy handover completes, arresting the driving carriage and transferring oscillation to the opposing unit before reversing.
Standard linear Simple Harmonic Motion (SHM) equations assume constant linear restoring forces and cannot capture the non-linear potential fields of close-proximity magnetic repulsion.
Simulation Scope & Open Scientific Frontiers
While this browser visualiser models the observable envelope of the 2.5-cycle handover, the complete analytical formulation of Active Magnetic Oscillation (AMO) remains an active research frontier. The mathematical complexities beyond the scope of this web model include:
Higher-Order Multipole Near-Field Repulsion: Standard dipole-dipole approximations (F∝r−4) underpredict the acceleration observed during close-proximity compression. Complete characterisation may require higher-order multipole expansions—including hypothetical quadrupole and octupole near-field contributions, governing the steep repulsive barrier.
Dynamic Potential-to-Kinetic Energy Conversion: Current numerical scripts illustrate kinetic energy (Ek) flow based on velocity vectors. They do not calculate the real-time conversion rates between stored electromagnetic potential energy (Umag) within the compressed magnetic boundary and the resulting kinetic output.
Inseparable Gravitational & Electromagnetic Potentials: In physical AMC motion, gravitational potential energy (Ug=mgh) and non-linear electromagnetic potential energy (Umag) act simultaneously across dynamic spatial coordinates. These coupled forces cannot be separated into independent, linear differential equations.
Non-Linear Decay & Carrier Period Invariance: Unlike classical contact restitution (where energy loss is governed by acoustic and frictional decay constants), magnetic damping involves multi-variable flux interactions. Furthermore, physical prototypes demonstrate an empirical carrier period invariance across variable swing amplitudes that linear damping models fail to predict.
Wavelet Architecture & Modulation Cadence: Real-world magnetometer telemetry exhibits deterministic wavelet packets and frequency-modulation cadences. Replicating these complex wavelets requires advanced spectral modeling tools beyond lightweight front-end browser runtimes.
For the mathematical formulations, time-frequency wavelets, and empirical kinematic datasets governing Active Magnetic Oscillation, explore our open-access research papers on Zenodo or view our Scientific Research Documentation →
Binary Newton's Cradle & AMC Telemetry
Compare classical mechanical sphere impacts with parallel-face Active Magnetic Cradle (AMC) dipole carriages.
Ek=0.50
AMO Oscillation Cadence: 
Slow Study
Binary Conservation (1 In → 1 Out):• Total Momentum (p = mv): In = 1.00 | Out = 1.00
• Total Kinetic Energy (Ek = ½mv²): In = 0.50 J | Out = 0.50 J
Classical Newton’s Cradle vs. Active Magnetic Cradle (AMC)
This interactive telemetry visualiser directly contrasts classical rigid-body collision mechanics with non-contact, field-coupled magnetic oscillations. By transitioning between classical elastic spheres and parallel-face magnetic dipole carriages within the same analytical framework, the tool demonstrates how energy conservation laws manifest differently across physical contact impacts versus continuous magnetic flux cushions.
Core Modes & Individual Tool Functionalities
1. Classical Rigid-Body Regimes (Ideal SHM vs. Contact Decay)
- Ideal Classical (SHM): Demonstrates textbook conservation of momentum (p = mv) and kinetic energy (Ek = ½mv²) across 1 to 4 sphere inputs. Collisions are treated as perfectly elastic (e = 1.0), transferring energy instantaneously at bottom-dead-centre without mechanical attenuation.
- Mechanical Contact Decay (e ≈ 0.95): Introduces real-world collision dynamics. Each mechanical impact dissipates ~8% to 10% of total system kinetic energy through acoustic shockwaves, Hertzian surface deformation, and localized thermal losses, driving the system toward rest over measurable cycles via the live Energy Retention bar.
2. The Conservation Paradox Demonstration
- Single-Ball Input vs. Multi-Ball Output: Evaluates the theoretical scenario where 1 sphere at velocity v attempts to eject 2 spheres at half velocity (0.5v).
- Mathematical Discrepancy: While total system momentum appears balanced (1.0 = 2 × 0.5), total kinetic energy drops by 50% (0.50 J → 0.25 J), visually proving via in-sphere telemetry why classical momentum cannot be conserved without satisfying quadratic kinetic energy constraints.
3. Real-Time Telemetry Mapping (Inside-the-Mass Readouts)
- Metric Switcher (p, Ek, or Both): Directly stamps real-time vector magnitudes inside the swinging masses rather than relying on detached external graphs.
- Phase-Locked Energy Handovers: Tracks instantaneous velocity scaling and energy handoffs at the exact moment of peak swing or central compression.
4. Active Magnetic Cradle (AMC) Coupled Dipole Mode
- Parallel-Face Bifilar Geometry: Transforms single-pivot spherical pendulums into two wide rectangular carriages suspended by twin parallel lines (bifilar linkage). This ensures the repelling South–South (S–S) faces remain strictly horizontal and parallel, completely eliminating vertical magnetic tilt shear.
- 2.5-Cycle Energy Handover: Replaces discrete collision impulses with a continuous, non-contact magnetic boundary. Driven by coupled magnetic flux repulsion, the system exchanges 50% of its kinetic energy over 2.5 carrier cycles (reaching phase equilibrium) and achieves a full 100% directional handover at 5.0 cycles before reversing.
5. Motion Controls & Variable Cadence Tuning
- Cadence Sweep (Slow Study ↔ Real-Time 2.46 Hz): An integrated continuous-phase slider scales the oscillation period from a deliberate study rate (0.60 Hz / 1650 ms) up to the empirical high-speed cadence (2.46 Hz / 406 ms) observed in physical AMC laboratory hardware.
- Phase Freeze (⏸ Pause to Read): Locks the carriages and spheres at peak displacement, allowing users to examine instantaneous telemetry, dipole alignments, and potential-to-kinetic distributions without tracking motion blur.
