Let this stand as the final proof: the robot that mastered the catwalk is built by a Chinese startup.
The journey continues, and we will advance, step by step.
@XPengMotors
Euler’s equation is one of the foundational ideas in fluid dynamics. It is essentially Newton’s second law written not for an individual particle but for an entire fluid. Instead of following each particle separately, the equation treats a fluid as a smooth distribution of density, pressure, and velocity, showing how its motion changes when forces act on it.
Euler’s equation says this:
“The acceleration of a fluid = the local change of its velocity + the change caused by the fluid moving through space = the forces from pressure differences + any external forces such as gravity.”
If pressure is uniform and there are no external forces, the fluid keeps moving exactly as it was, just like a collection of particles obeying Newton’s laws. Pressure gradients push the fluid around.
Gravity accelerates it. And the way the velocity changes depends not only on what happens at one point, but also on how the fluid moves into regions with different velocities.
In astrophysics, Euler’s equation appears everywhere. It describes how gas collapses under gravity to form stars, how shock waves expand after supernovae, how accretion disks evolve around black holes, how the intracluster medium flows inside galaxy clusters, and how the matter in the cosmos moves on large scales. In cosmology, dark matter is often treated as a pressureless fluid.
In that case, Euler’s equation becomes even simpler: the motion of dark matter changes only because of gravity. This simplified version is exactly the one used in large-scale structure simulations like the study I've posted before.
When galaxies, which trace dark matter, fall into cosmic gravity wells following Euler’s equation, it suggests that dark matter behaves like a collisionless fluid governed solely by gravity, with no extra “fifth force” acting on it.
Euler’s equation is closely tied to conservation laws. When combined with mass conservation and an equation of state, it forms a complete system describing the full evolution of a fluid.
Many familiar results come from special cases of Euler’s equation: hydrostatic equilibrium in stars, where pressure balances gravity; and Bernoulli’s principle, which links pressure and velocity along a flow.
Because Euler’s equation ignores viscosity, it is mathematically clean and often solvable in elegant ways, yet still capable of producing nonlinear behavior, shocks, and instabilities when the flow becomes complex.
Euler’s equation describes an ideal fluid, one without viscosity, because it isolates the fundamental effects of pressure and external forces on motion. When viscosity matters, we use the more general Navier–Stokes equation, which is basically Euler’s equation plus the viscous terms. Many astrophysical systems, like dark matter or large-scale cosmic flows, behave effectively like non-viscous fluids, so Euler is the appropriate model there
It is the backbone of classical fluid motion, the starting point for more advanced theories like magnetohydrodynamics and relativistic hydrodynamics, and a central tool in understanding everything from ocean currents to galaxy formation.
Euler’s equation is Newtonian mechanics applied to a continuous medium, one of the simplest and most powerful equations in physics, and absolutely essential in astrophysics and cosmology.
The three-body problem is a classic and notoriously difficult question in physics and mathematics. It asks: How do three objects, such as stars, planets, or moons, move under the influence of each other’s gravity? Unlike the simpler two-body problem, which has precise and predictable analytical solutions (like the Earth orbiting the Sun in an ellipse), the three-body problem quickly becomes chaotic and unpredictable.
This complexity arises because each object's motion constantly affects, and is affected by, the other two. These gravitational interactions form a tangled and unstable system. In fact, there's no general formula that can solve all three-body scenarios exactly. This was first demonstrated in the 19th century by Henri Poincaré, whose work laid the foundations for chaos theory.
While exact solutions remain elusive, scientists have discovered certain special cases where the motion is stable or periodic. One well-known example is the Lagrange points, where three bodies can maintain a stable triangular configuration. However, such neat solutions are rare.
Today, thanks to powerful computers, researchers can simulate three-body systems with remarkable accuracy, helping us study triple-star systems, exoplanets, and asteroid dynamics. Yet even small changes in the starting conditions can lead to dramatically different outcomes, highlighting the sensitive dependence on initial conditions that defines chaotic systems.
The three-body problem is actually a specific case of the broader n-body problem, where n can be any number of interacting bodies. As n increases, the complexity and unpredictability rise even further.
The three-body problem serves as a vivid example of how simple laws of nature, like Newton’s law of gravity, can produce behavior that is intricate, unexpected, and profoundly difficult to predict.
Figure's robot, powered by the Helix neural network, can move packages like a human.
The policy is flipping packages to orientate the barcode down - it has learned to flatten packages for the scanner
#engineering#technology#robotics#robots
Video Credit: @adcock_brett
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You've probably seen my Pale Blue Dot image – but what about this one, which I snapped years prior, just 13 days after I launched?
It was the first image ever taken of the entire Earth and Moon together. -V1
An extraordinarily rare photograph captures the precise moment Saturn emerges from behind the Moon.
This celestial alignment typically only occurs once every five years.
📸 Paul Stewart
The International @Space_Station, home to seven humans living and working in space, crosses in front of the 56.9%-illuminated Moon at 5:25:45.61 pm ET today, as seen from South Florida 🛰️🌓