Gravity and Friction

// From PhysicsUpdate.tsx line 101
const g_val = grav ? 9.80665 : 0;
//                   ^^^^^^^^ standard gravity in m/s²

// From PhysicsUpdate.tsx lines 119-123
const nz = p.p0_fis[2] + 
  evaluarFormula(p.fz, nt, live.pos[0], live.pos[1], live.pos[2]) + 
  p.v0_fis[2] * nt - 
  0.5 * g_val * Math.pow(nt, 2);
  //    ^^^^^^^^^^^^^^^^^^^^^^^
  //    Classic kinematic equation: Δz = v₀t - ½gt²

// From PhysicsUpdate.tsx lines 177-251
const m = p.mass || 0.001;
const peso = m * g_val; // Weight force = mg

// Gravity contributes to Z-acceleration
accNew = [
  fuerzaResultanteX / m,
  fuerzaResultanteY / m,
  fuerzaResultanteZ / m - g_val,  // a_z = F_z/m - g
];

// From PhysicsUpdate.tsx line 181
const enSuelo = posFinal[2] <= 0;
//                        ^
//                        Physics Z-coordinate

// From PhysicsUpdate.tsx lines 188-189
if (enSuelo) {
  posFinal[2] = 0;  // Clamp to ground level
  // ...
}

// From PhysicsUpdate.tsx lines 289-293
if (posFinal[2] <= 0) {
  posFinal[2] = 0;
  if (velFinal[2] < 0) velFinal[2] = 0;  // No downward velocity
}

// From PhysicsUpdate.tsx lines 179-195
const enSuelo = posFinal[2] <= 0;
let normal = 0;

if (enSuelo) {
  // Normal = |min(0, ΣFz - peso)|
  // If ΣFz - peso < 0 → force pressing against ground → normal exists
  // If ΣFz - peso >= 0 → object being lifted → no normal
  const fuerzaNetoZ = sumF[2] - peso;
  normal = Math.abs(Math.min(0, fuerzaNetoZ));
}

// Example 1: Resting on ground with no applied forces
sumF[2] = 0
peso = 10 N
fuerzaNetoZ = 0 - 10 = -10 N
normal = |-10| = 10 N  // Normal balances weight

// Example 2: Being pushed down by additional force
sumF[2] = -5 N  // 5 N downward force applied
peso = 10 N
fuerzaNetoZ = -5 - 10 = -15 N
normal = |-15| = 15 N  // Normal balances weight + applied force

// Example 3: Being pulled up
sumF[2] = +15 N  // 15 N upward force applied
peso = 10 N
fuerzaNetoZ = +15 - 10 = +5 N
normal = |0| = 0 N  // No normal force, particle lifts off ground

// From Escenario.tsx line 31
const [friction, setFriction] = useState(0.2);
//                                       ^^^^ default μ = 0.2

// From PhysicsUpdate.tsx lines 197-239
if (enSuelo) {
  if (normal > 0 && friction > 0) {
    // Maximum friction force = μ * N
    const friccionMax = friction * normal;
    
    // Determine if object is moving or at rest
    const vx = live.vel[0];
    const vy = live.vel[1];
    const vHor = Math.hypot(vx, vy);  // Horizontal velocity magnitude
    
    if (vHor > 1e-9) {
      // KINETIC FRICTION: Object is moving
      // ...
    } else if (fuerzaHorizontal > 1e-9) {
      // STATIC FRICTION: Object at rest with applied force
      // ...
    }
  }
}

// From PhysicsUpdate.tsx lines 210-224
if (vHor > 1e-9) {
  // Object is moving: kinetic friction
  // Friction opposes velocity
  const dirX = vx / vHor; // Unit direction of velocity in X
  const dirY = vy / vHor; // Unit direction of velocity in Y
  
  // If max friction > applied force + momentum,
  // friction equals force (object decelerates to stop)
  // Otherwise use max friction
  const friccionAplicada = Math.min(
    friccionMax, 
    fuerzaHorizontal + m * vHor / dT
  );
  
  // Decompose friction into X and Y (opposite to velocity)
  friccionX = -dirX * friccionAplicada;
  friccionY = -dirY * friccionAplicada;
}

// From PhysicsUpdate.tsx lines 225-238  
else if (fuerzaHorizontal > 1e-9) {
  // Object at rest but forces applied: static friction
  // Friction opposes applied force
  const dirFx = sumF[0] / fuerzaHorizontal;
  const dirFy = sumF[1] / fuerzaHorizontal;
  
  // If max friction > applied force,
  // friction cancels force completely (no movement)
  // Otherwise use max friction
  const friccionAplicada = Math.min(friccionMax, fuerzaHorizontal);
  
  friccionX = -dirFx * friccionAplicada;
  friccionY = -dirFy * friccionAplicada;
}

// From PhysicsUpdate.tsx lines 242-252
// Resultant force = Applied forces + Friction
const fuerzaResultanteX = sumF[0] + friccionX;
const fuerzaResultanteY = sumF[1] + friccionY;
const fuerzaResultanteZ = sumF[2];

// New acceleration a(t+dt)  
accNew = [
  fuerzaResultanteX / m,
  fuerzaResultanteY / m,
  fuerzaResultanteZ / m - g_val,
];

// Initial conditions
mass = 2 kg
velocity = [5, 0, 0] m/s  // Moving right at 5 m/s
position = [0, 0, 0]      // On the ground
friction = 0.3            // μ = 0.3
gravity = 9.80665 m/s²

// Frame 1:
// ---------
// Ground detection
enSuelo = (0 <= 0) = true  ✓

// Normal force
peso = 2 * 9.80665 = 19.613 N
sumF = [0, 0, 0]  // No applied forces
fuerzaNetoZ = 0 - 19.613 = -19.613 N
normal = |-19.613| = 19.613 N

// Friction (kinetic, since moving)
friccionMax = 0.3 * 19.613 = 5.884 N
vHor = 5 m/s > 1e-9  ✓ kinetic friction
dirX = 5 / 5 = 1  (moving right)
friccionAplicada = 5.884 N
friccionX = -1 * 5.884 = -5.884 N  (opposes motion)

// Acceleration
accNew[0] = -5.884 / 2 = -2.942 m/s²

// Velocity update (assuming dt = 0.01 s)
velFinal[0] = 5 + (-2.942) * 0.01 = 4.97 m/s

// The particle is slowing down due to friction

// Eventually:
vHor < 1e-9  // Very small velocity
// Particle stops, friction transitions to static

// From PhysicsUpdate.tsx lines 270-286
if (enSuelo && normal > 0) {
  const vHorFinal = Math.hypot(velFinal[0], velFinal[1]);
  const fuerzaHorizontalNeta = Math.hypot(
    fuerzaResultanteX, 
    fuerzaResultanteY
  );
  
  // If velocity is tiny and net force is tiny, stop completely
  if (vHorFinal < 1e-6 && fuerzaHorizontalNeta < 1e-6) {
    velFinal[0] = 0;
    velFinal[1] = 0;
  }
  
  // Vertical velocity cannot be negative on ground
  if (velFinal[2] < 0) {
    velFinal[2] = 0;
  }
}