2D Physics

Collaboration diagram for 2D Physics:

Data Structures
struct	bj_particle_2d
struct	bj_angular_2d
struct	bj_rigid_body_2d

Functions
struct bj_vec2	bj_compute_kinematics_2d (struct bj_vec2 position, struct bj_vec2 velocity, struct bj_vec2 acceleration, bj_real time)
struct bj_vec2	bj_compute_kinematics_velocity_2d (struct bj_vec2 velocity, struct bj_vec2 acceleration, bj_real time)
void	bj_apply_particle_force_2d (struct bj_particle_2d *particle, const struct bj_vec2 force)
void	bj_step_particle_2d (struct bj_particle_2d *particle, bj_real dt)
void	bj_apply_gravity_2d (struct bj_particle_2d *particle, bj_real gravity)
void	bj_apply_point_gravity_2d (struct bj_particle_2d *restrict particle_from, const struct bj_particle_2d *restrict particle_to, const bj_real gravity_factor)
void	bj_apply_point_gravity_softened_2d (struct bj_particle_2d *restrict particle_from, const struct bj_particle_2d *restrict particle_to, const bj_real gravity_factor, const bj_real epsilon)
void	bj_apply_drag_2d (struct bj_particle_2d *particle, bj_real k1, bj_real k2)
bj_real	bj_compute_particle_drag_coefficient_2d (const struct bj_vec2 vel, const bj_real k1, const bj_real k2)
struct bj_vec2	bj_compute_particle_drag_force_2d (struct bj_vec2 vel, const bj_real k1, const bj_real k2)
void	bj_apply_angular_torque_2d (struct bj_angular_2d *angular, bj_real torque)
void	bj_step_angular_2d (struct bj_angular_2d *angular, double delta_time)
void	bj_apply_rigidbody_force_2d (struct bj_rigid_body_2d *body, const struct bj_vec2 force)
void	bj_step_rigid_body_2d (struct bj_rigid_body_2d *body, double delta_time)

Detailed Description

2D physics utilities (point masses, forces, kinematics).

This header provides small helpers for common 2D physics operations. By default, quantities are interpreted in SI units (meters, seconds), but formulas are dimensionally homogeneous: results are correct for any consistent unit system (e.g., km and s; cm and s), provided all inputs use the same system.

Dimensionality uses the base dimensions L (length) and T (time). For example:

• position: [L]
• velocity: [L T^-1]
• acceleration: [L T^-2]
• time: [T]

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Data Structure Documentation

bj_particle_2d

struct bj_particle_2d

2D point mass state and physical properties.

Positions, velocities, accelerations and force accumulator are expressed in world space. Damping is a unitless velocity decay factor applied per-step. Mass is represented as inverse mass; use 0 to represent an immovable object.

Parameters

position	Current 2D position [L]
velocity	Current 2D velocity [L T^-1]
acceleration	Current 2D acceleration [L T^-2]
forces	Accumulated force for the next integration step [M L T^-2]
damping	Velocity damping factor in [0, 1]
inverse_mass	Inverse of mass [M^-1]; 0 means infinite mass

Collaboration diagram for bj_particle_2d:

Data Fields
struct bj_vec2	acceleration
bj_real	damping
struct bj_vec2	forces
bj_real	inverse_mass
struct bj_vec2	position
struct bj_vec2	velocity

bj_angular_2d

struct bj_angular_2d

Angular.

2D angular state and properties (scalar angle about Z).

Angle units are radians. Damping is unitless per-step decay on angular velocity. Inertia is represented via inverse inertia; use 0 for infinite inertia.

Parameters

value	Angle theta [rad]
velocity	Angular velocity omega [rad T^-1]
acceleration	Angular acceleration alpha [rad T^-2]
torque	Accumulated torque tau for next step [M L^2 T^-2]
damping	Angular velocity damping factor in [0, 1]
inverse_inertia	Inverse moment of inertia I^-1 [M^-1 L^-2]

Data Fields
bj_real	acceleration
bj_real	damping
bj_real	inverse_inertia
bj_real	torque
bj_real	value
bj_real	velocity

bj_rigid_body_2d

struct bj_rigid_body_2d

Rigid body with translational and angular components.

Particle terms are in world space. Angle is about +Z.

Parameters

particle	Linear state (position, velocity, forces)
angular	Angular state (theta, omega, tau)

Collaboration diagram for bj_rigid_body_2d:

Data Fields
struct bj_angular_2d	angular
struct bj_particle_2d	particle

Function Documentation

bj_apply_angular_torque_2d()

void bj_apply_angular_torque_2d	(	struct bj_angular_2d *	angular,
		bj_real	torque )

Add torque to the angular accumulator.

Parameters

angular	Angular state to modify
torque	Torque to add tau [M L^2 T^-2]

bj_apply_drag_2d()

void bj_apply_drag_2d	(	struct bj_particle_2d *	particle,
		bj_real	k1,
		bj_real	k2 )

Apply quadratic + linear drag to a particle's accumulator.

Drag magnitude = k1 * |v| + k2 * |v|^2 along -v_hat.

Parameters

particle	Particle to affect
k1	Linear drag coefficient [M T^-1]
k2	Quadratic drag coefficient [M L^-1]

bj_apply_gravity_2d()

void bj_apply_gravity_2d	(	struct bj_particle_2d *	particle,
		bj_real	gravity )

Apply constant downward gravity in world space to a particle.

Adds force F = m * g * (0, -1) assuming -Y is "down".

Parameters

particle	Particle to affect
gravity	Gravitational acceleration magnitude g >= 0 [L T^-2]

bj_apply_particle_force_2d()

void bj_apply_particle_force_2d	(	struct bj_particle_2d *	particle,
		const struct bj_vec2	force )

Add a force to a particle's accumulator.

The force will be used on the next integration step, then should be cleared by the step routine.

Parameters

particle	Particle to modify
force	Force to add [M L T^-2]

bj_apply_point_gravity_2d()

void bj_apply_point_gravity_2d	(	struct bj_particle_2d *restrict	particle_from,
		const struct bj_particle_2d *restrict	particle_to,
		const bj_real	gravity_factor )

Apply point gravity from one particle to another.

Adds a Newtonian attraction from particle_to to particle_from. Uses F = Gm1m2 r_hat / r^2 with gravity_factor = G.

Parameters

particle_from	Particle receiving the force
particle_to	Source particle
gravity_factor	Gravitational constant G [L^3 M^-1 T^-2]

bj_apply_point_gravity_softened_2d()

void bj_apply_point_gravity_softened_2d	(	struct bj_particle_2d *restrict	particle_from,
		const struct bj_particle_2d *restrict	particle_to,
		const bj_real	gravity_factor,
		const bj_real	epsilon )

Apply softened point gravity to avoid singularities at small r.

Uses F proportional to r / (r^2 + epsilon^2)^(3/2).

Parameters

particle_from	Particle receiving the force
particle_to	Source particle
gravity_factor	Gravitational constant G [L^3 M^-1 T^-2]
epsilon	Softening length epsilon >= 0 [L]

bj_apply_rigidbody_force_2d()

void bj_apply_rigidbody_force_2d	(	struct bj_rigid_body_2d *	body,
		const struct bj_vec2	force )

Apply a world-space force at the center of mass.

Only affects linear state. Use external torque to affect rotation.

Parameters

body	Rigid body to modify
force	Force to add [M L T^-2]

bj_compute_kinematics_2d()

struct bj_vec2 bj_compute_kinematics_2d	(	struct bj_vec2	position,
		struct bj_vec2	velocity,
		struct bj_vec2	acceleration,
		bj_real	time )

Integrate constant-acceleration 2D kinematics: position at time t.

Uses: out = position + velocity * time + 0.5 * acceleration * time^2.

Parameters

position	Initial position [L]
velocity	Initial velocity [L T^-1]
acceleration	Constant acceleration [L T^-2]
time	Elapsed time t [T]

Returns

Output position at time t [L]

bj_compute_kinematics_velocity_2d()

struct bj_vec2 bj_compute_kinematics_velocity_2d	(	struct bj_vec2	velocity,
		struct bj_vec2	acceleration,
		bj_real	time )

Integrate constant-acceleration 2D kinematics: velocity at time t.

Uses: out = velocity + acceleration * time.

Parameters

velocity	Initial velocity [L T^-1]
acceleration	Constant acceleration [L T^-2]
time	Elapsed time t [T]

Returns

Output velocity at time t [L T^-1]

bj_compute_particle_drag_coefficient_2d()

bj_real bj_compute_particle_drag_coefficient_2d	(	const struct bj_vec2	vel,
		const bj_real	k1,
		const bj_real	k2 )

Return scalar drag coefficient for a velocity.

Computes c = k1 * |v| + k2 * |v|^2.

Parameters

vel	Velocity vector [L T^-1]
k1	Linear drag coefficient [M T^-1]
k2	Quadratic drag coefficient [M L^-1]

Returns

c >= 0 [M T^-1]

bj_compute_particle_drag_force_2d()

struct bj_vec2 bj_compute_particle_drag_force_2d	(	struct bj_vec2	vel,
		const bj_real	k1,
		const bj_real	k2 )

Compute drag force for a velocity.

result = -c * v_hat with c as above. Zero if vel is near zero.

Parameters

vel	Velocity vector [L T^-1]
k1	Linear drag coefficient [M T^-1]
k2	Quadratic drag coefficient [M L^-1]

Returns

Output force [M L T^-2]

bj_step_angular_2d()

void bj_step_angular_2d	(	struct bj_angular_2d *	angular,
		double	delta_time )

Semi-implicit Euler step for angular motion.

Integrates alpha and omega, applies damping, and advances theta. Clears torque.

Parameters

angular	Angular state to integrate
delta_time	Time step [T]

bj_step_particle_2d()

void bj_step_particle_2d	(	struct bj_particle_2d *	particle,
		bj_real	dt )

Semi-implicit Euler step for a particle.

Integrates acceleration and velocity, applies damping, and advances position. Clears the force accumulator after use.

Parameters

particle	Particle to integrate
dt	Time step [T]

bj_step_rigid_body_2d()

void bj_step_rigid_body_2d	(	struct bj_rigid_body_2d *	body,
		double	delta_time )

Step rigid body linear and angular states.

Calls the corresponding particle and angular integrators. Clears accumulators.

Parameters

body	Rigid body to integrate
delta_time	Time step [T]