### Basic 3D Physics Scene Setup

Source: https://github.com/avianphysics/avian/blob/main/README.md

Sets up a Bevy application with Avian physics, including a static platform and a dynamic cube with initial angular velocity.

```rust
use avian3d::prelude::*;
use bevy::prelude::*;

fn main() {
    App::new()
        // Enable physics
        .add_plugins((DefaultPlugins, PhysicsPlugins::default()))
        .add_systems(Startup, setup)
        .run();
}

fn setup(
    mut commands: Commands,
    mut meshes: ResMut<Assets<Mesh>>,
    mut materials: ResMut<Assets<StandardMaterial>>,
) {
    // Static physics object with a collision shape
    commands.spawn(( 
        RigidBody::Static,
        Collider::cylinder(4.0, 0.1),
        Mesh3d(meshes.add(Cylinder::new(4.0, 0.1))),
        MeshMaterial3d(materials.add(Color::WHITE)),
    ));

    // Dynamic physics object with a collision shape and initial angular velocity
    commands.spawn(( 
        RigidBody::Dynamic,
        Collider::cuboid(1.0, 1.0, 1.0),
        AngularVelocity(Vec3::new(2.5, 3.5, 1.5)),
        Mesh3d(meshes.add(Cuboid::from_length(1.0))),
        MeshMaterial3d(materials.add(Color::srgb_u8(124, 144, 255))),
        Transform::from_xyz(0.0, 4.0, 0.0),
    ));

    // Light
    commands.spawn(( 
        PointLight {
            shadows_enabled: true,
            ..default()
        },
        Transform::from_xyz(4.0, 8.0, 4.0),
    ));

    // Camera
    commands.spawn(( 
        Camera3d::default(),
        Transform::from_xyz(-2.5, 4.5, 9.0).looking_at(Vec3::ZERO, Dir3::Y),
    ));
}
```

--------------------------------

### Markdown Example for Migration Guide Section

Source: https://github.com/avianphysics/avian/blob/main/migration-guides/README.md

Example of how to structure a section in a migration guide, including a title and associated PRs.

```markdown
## Sleeping and Simulation Islands

PRs: [#809](https://github.com/avianphysics/avian/pull/809)

Content goes here
```

--------------------------------

### Running f64 Precision Examples

Source: https://github.com/avianphysics/avian/blob/main/README.md

Command to run examples with f64 precision by disabling default features and specifying features manually.

```shell
cargo run --example cubes --no-default-features --features "3d f64 parry-f64"
```

--------------------------------

### Rust Deprecated Attribute Example

Source: https://github.com/avianphysics/avian/blob/main/migration-guides/README.md

Demonstrates the usage of the `#[deprecated]` attribute in Rust to mark code as obsolete. This attribute downgrades errors to warnings and provides migration information in IDEs.

```rust
#[deprecated(since = "0.4.0", note = "This message will appear in the deprecation warning.")]
struct MyStruct;
```

--------------------------------

### Calculate Stiffness and Damping from Frequency and Damping Ratio

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

These formulas demonstrate how to derive stiffness and damping coefficients using effective mass, frequency (omega), and damping ratio (zeta).

```rust
let stiffness = effective_mass * omega * omega;
let damping = 2.0 * effective_mass * zeta * omega;
```

--------------------------------

### Run specific benchmark configuration

Source: https://github.com/avianphysics/avian/blob/main/benches/README.md

Executes the 'Large Pyramid 2D' benchmark with a specified thread range, step count, and repetition count.

```shell
# Note: Make sure `benches` is the active working directory
cargo run -- --name "Large Pyramid 2D" --threads 1..=6 --steps 500 --repeat 5
```

--------------------------------

### Calculate CFM and ERP from Stiffness and Damping

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

These formulas show how to compute CFM and ERP based on stiffness and damping values, which are common in physics simulations.

```rust
let cfm = 1.0 / (delta_time * stiffness + damping);
let erp = (delta_time * stiffness) / (delta_time * stiffness + damping);
```

--------------------------------

### Add Avian Physics Dependency

Source: https://github.com/avianphysics/avian/blob/main/README.md

Add this to your Cargo.toml to use the latest version from the main branch.

```toml
[dependencies]
avian3d = { git = "https://github.com/avianphysics/avian", branch = "main" }
```

--------------------------------

### Calculate Soft Constraint Parameters

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

Calculates coefficients for soft constraints based on damping ratio, frequency, and time step. These parameters are used to tune the stability and response of constraints.

```rust
let zeta = 1.0;               // Damping ratio (controls the amount of oscillation)
let hertz = 5.0;              // Frequency (cycles per second)
let omega = 2.0 * PI * hertz; // Angular frequency (controls the rate of oscillation)

// Shared expressions
let a1 = 2.0 * zeta + omega * delta_time;
let a2 = omega * delta_time * a1;
let a3 = 1.0 / (1.0 + a2);

// Coefficients
let bias_coefficient = omega / a1;
let mass_coefficient = a2 * a3;
let impulse_coefficient = a3;
```

--------------------------------

### Migrating Collision Event Handling

Source: https://github.com/avianphysics/avian/blob/main/migration-guides/README.md

Demonstrates the transition from version 0.3 to 0.4 for collision event readers, highlighting the change from EventReader to MessageReader and the updated event structure.

```rust
// 0.3
fn print_started_collisions(mut collision_reader: EventReader<CollisionStarted>) {
    for CollisionStarted(collider1, collider2) in collision_reader.read() {
        println!("{collider1} and {collider2} started colliding");
    }
}

// 0.4
fn print_started_collisions(mut collision_reader: MessageReader<CollisionStart>) {
    // Note: The event now also stores `body1` and `body2`
    for event in collision_reader.read() {
        println!("{} and {} started colliding", event.collider1, event.collider2);
    }
}
```

--------------------------------

### Run benchmarks by dimension

Source: https://github.com/avianphysics/avian/blob/main/benches/README.md

Executes benchmarks filtered by 2D or 3D features using cargo flags.

```shell
# List all 2D benchmarks
cargo run --no-default-features --features 2d -- --list

# Run all 3D benchmarks with default options
cargo run --no-default-features --features 3d
```

--------------------------------

### Add Avian3D Dependency

Source: https://github.com/avianphysics/avian/blob/main/README.md

Add the avian3d crate to your Cargo.toml file for 3D applications.

```toml
# For 3D applications:
[dependencies]
avian3d = "0.6"
```

--------------------------------

### Add Avian2D Dependency

Source: https://github.com/avianphysics/avian/blob/main/README.md

Add the avian2d crate to your Cargo.toml file for 2D applications.

```toml
# For 2D applications:
[dependencies]
avian2d = "0.6"
```

--------------------------------

### Compute Contact Impulse with Soft Constraints

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

Calculates the incremental impulse for a contact constraint using soft constraints. This method incorporates softness parameters for stable and controlled response.

```rust
let biased_normal_speed = normal_speed + bias_coefficient * separation;
let scaled_effective_mass = mass_coefficient * effective_mass;
let extra_impulse = impulse_coefficient * accumulated_impulse;

let incremental_impulse = -scaled_effective_mass * biased_normal_speed - extra_impulse;
```

--------------------------------

### Compute Contact Impulse (PGS)

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

Calculates the incremental impulse for a contact constraint using Projected Gauss-Seidel (PGS) without stabilization. This is a baseline for impulse calculation.

```rust
let incremental_impulse = -effective_mass * normal_speed;
```

--------------------------------

### Define RigidBodyForces Traits

Source: https://github.com/avianphysics/avian/blob/main/migration-guides/0.5-to-0.6.md

Defines `ReadRigidBodyForces` and `WriteRigidBodyForces` traits, with `RigidBodyForces` combining both. Use these traits if your implementation of `RigidBodyForces` needs adjustments.

```rust
pub trait RigidBodyForces: ReadRigidBodyForces + WriteRigidBodyForces {}

```

--------------------------------

### Compute Contact Impulse with Baumgarte Stabilization

Source: https://github.com/avianphysics/avian/blob/main/src/dynamics/solver/softness_parameters/README.md

Calculates the incremental impulse for a contact constraint with Baumgarte stabilization. An additional bias term is added to correct for penetration depth.

```rust
let bias = bias_factor / delta_time * penetration_depth.max(0.0);
let incremental_impulse = -effective_mass * (normal_speed + bias);
```

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