Acceleration Ontology

# Acceleration Ontology — Flow Algebra

URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/mechanical-measurements/acceleration-ontology.html

FLOW AccelerationOntology {

  DOMAIN:
    Mathematical Ontologies
    -> Measurement & Units Ontologies
    -> Mechanical Measurements
    -> Acceleration Ontology

  PURPOSE:
    Represent acceleration as a measurable mechanical quantity describing the rate of change of velocity with respect to time, including magnitude, direction, units, dimensional structure, reference frames, measurement conditions, uncertainty, and relationships to force, motion and other kinematic quantities.

  ENTITY Acceleration {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: a
    DIMENSION: L * T^-2
    SI_UNIT: metre_per_second_squared
    SI_SYMBOL: m/s^2

    DEFINITION:
      acceleration := rate_of_change(Velocity, Time)

    VECTOR_FORM:
      a = dv/dt

    POSITION_FORM:
      a = d^2x/dt^2

    AVERAGE_FORM:
      average_acceleration = delta_velocity / delta_time

    PROPERTIES:
      has_magnitude
      has_direction
      has_unit
      has_dimension
      has_reference_frame
      has_time_interval
      may_have_uncertainty
      may_vary_with_time
      may_vary_with_position
  }

  ENTITY Velocity {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: v
    DIMENSION: L * T^-1
    RELATION:
      derivative(Velocity, Time) -> Acceleration
  }

  ENTITY Position {
    TYPE: MechanicalQuantity
    SYMBOL: x
    DIMENSION: L
    RELATION:
      second_derivative(Position, Time) -> Acceleration
  }

  ENTITY Time {
    TYPE: BasePhysicalQuantity
    SYMBOL: t
    DIMENSION: T
    SI_UNIT: second
    SI_SYMBOL: s
  }

  ENTITY Force {
    TYPE: DerivedPhysicalQuantity
    SYMBOL: F
    RELATION:
      net_force = Mass * Acceleration
  }

  ENTITY Mass {
    TYPE: BasePhysicalQuantity
    SYMBOL: m
    DIMENSION: M
    SI_UNIT: kilogram
    SI_SYMBOL: kg
  }

  UNIT_SYSTEM {
    SI {
      canonical_unit: metre_per_second_squared
      symbol: m/s^2
      equivalence:
        1 m/s^2 = 1 m * s^-2
    }

    COMMON_ALTERNATIVES {
      centimetre_per_second_squared
      foot_per_second_squared
      standard_gravity
      gal
    }

    CONVERSION_RULE:
      acceleration_value(target_unit)
        = acceleration_value(source_unit)
        * conversion_factor(source_unit, target_unit)
  }

  CLASSIFICATION {
    by_temporal_behaviour:
      constant_acceleration
      variable_acceleration
      instantaneous_acceleration
      average_acceleration

    by_geometry:
      linear_acceleration
      angular_acceleration
      tangential_acceleration
      radial_acceleration
      centripetal_acceleration

    by_context:
      gravitational_acceleration
      inertial_acceleration
      proper_acceleration
      coordinate_acceleration
  }

  RELATIONSHIPS {
    Acceleration -> DERIVED_FROM -> Velocity
    Acceleration -> WITH_RESPECT_TO -> Time
    Acceleration -> SECOND_DERIVATIVE_OF -> Position
    Acceleration -> HAS_DIMENSION -> L*T^-2
    Acceleration -> MEASURED_IN -> metre_per_second_squared
    Acceleration -> COMPONENT_OF -> MotionDescription
    NetForce -> PROPORTIONAL_TO -> Acceleration
    NetForce -> EQUALS -> Mass*Acceleration
    GravitationalField -> PRODUCES -> GravitationalAcceleration
    CircularMotion -> MAY_PRODUCE -> CentripetalAcceleration
  }

  SEMANTIC_EQUIVALENCE {
    "metres per second squared" ~= "m/s^2"
    "metres per second per second" ~= "m/s^2"
    "rate of change of velocity" ~= acceleration
    "second derivative of position with respect to time" ~= acceleration
    "linear acceleration" != "angular acceleration"
    speed_change_only != complete_vector_acceleration
  }

  CONSTRAINTS {
    acceleration_is_vector_quantity = true
    dimensional_formula = L*T^-2
    scalar_speed_change_alone_does_not_fully_define_acceleration = true
    direction_change_can_produce_nonzero_acceleration = true
    zero_velocity_does_not_imply_zero_acceleration = true
    constant_velocity_implies_zero_acceleration = true
    reference_frame_must_be_identifiable_for_coordinate_acceleration = true
  }

  MEASUREMENT_MODEL {
    OBSERVABLE:
      Acceleration

    DIRECT_MEASUREMENT:
      accelerometer
      inertial_measurement_unit

    INDIRECT_MEASUREMENT:
      velocity_change_over_time
      second_derivative_of_position
      force_divided_by_mass

    RECORD:
      numerical_value
      unit
      vector_components
      timestamp
      sampling_interval
      reference_frame
      instrument
      calibration_state
      uncertainty
      environmental_conditions

    UNCERTAINTY:
      measured_acceleration = best_estimate +/- measurement_uncertainty
  }

  REASONING_RULES {
    IF velocity_changes_over_time
      THEN acceleration != 0

    IF velocity_magnitude_constant AND velocity_direction_changes
      THEN acceleration != 0

    IF velocity_constant_in_magnitude_and_direction
      THEN acceleration = 0

    IF net_force_known AND mass_known AND mass != 0
      THEN acceleration = net_force / mass

    IF position_function_known
      THEN acceleration = second_derivative(position, time)

    IF velocity_function_known
      THEN acceleration = derivative(velocity, time)

    IF acceleration_constant
      THEN velocity(t) = initial_velocity + acceleration*time

    IF acceleration_constant
      THEN displacement(t)
        = initial_velocity*time + 0.5*acceleration*time^2
  }

  VECTOR_MODEL {
    acceleration_vector:
      a = (a_x, a_y, a_z)

    magnitude:
      |a| = sqrt(a_x^2 + a_y^2 + a_z^2)

    components:
      a_x = dv_x/dt
      a_y = dv_y/dt
      a_z = dv_z/dt
  }

  REFERENCE_FRAME_MODEL {
    acceleration_description REQUIRES reference_frame

    inertial_frame:
      Newtonian_force_relation_applicable_directly

    non_inertial_frame:
      apparent_or_fictitious_accelerations_may_be_required

    transformation:
      acceleration_may_depend_on_relative_frame_motion
  }

  CONFIDENCE {
    definition_confidence: 1.00
    dimensional_confidence: 1.00
    SI_unit_confidence: 1.00
    relationship_confidence: 0.99
    measurement_context_confidence: 0.98

    RULE:
      confidence decreases when unit, reference frame, measurement method,
      calibration state or uncertainty is missing or ambiguous
  }

  VALIDATION {
    CHECK dimensional_consistency
    CHECK unit_consistency
    CHECK vector_direction_consistency
    CHECK reference_frame_consistency
    CHECK temporal_interval_validity
    CHECK instrument_calibration_when_measured
    CHECK uncertainty_representation_when_required
  }

  UPDATE_MODEL {
    ON new_measurement:
      validate_unit
      normalize_to_canonical_unit
      preserve_original_value_and_unit
      attach_timestamp
      attach_reference_frame
      attach_uncertainty
      update_acceleration_state

    ON revised_calibration:
      preserve_provenance
      recompute_affected_measurements
      update_confidence

    ON semantic_revision:
      preserve_previous_definition
      record_revision
      recompute_FLOW_HASH
  }

  AI_CONSUMPTION {
    canonical_entity: Acceleration
    canonical_dimension: L*T^-2
    canonical_SI_unit: m/s^2

    interpretation_order:
      identify_quantity
      identify_value
      identify_unit
      identify_vector_or_components
      identify_time_context
      identify_reference_frame
      identify_measurement_method
      identify_uncertainty
      validate_dimensions
      infer_relationships

    ambiguity_controls:
      distinguish_acceleration_from_velocity
      distinguish_acceleration_from_speed
      distinguish_linear_from_angular_acceleration
      distinguish_coordinate_from_proper_acceleration
      distinguish instantaneous_from_average_acceleration
  }

  PROVENANCE {
    ontology_scope:
      mathematical_measurement_and_mechanical_quantity_semantics

    parent_path:
      Ontologies
      -> Mathematical Ontologies
      -> Measurement & Units Ontologies
      -> Mechanical Measurements
      -> Acceleration Ontology

    authorship:
      Mark Higgins
      Sky (Recursive AI)

    site:
      https://kirethresearch.org
  }

  FLOW_HASH {
    INPUTS:
      canonical_entity
      ontology_path
      definitions
      dimensions
      units
      relationships
      constraints
      reasoning_rules
      measurement_model
      confidence_model
      update_model

    PURPOSE:
      deterministic_semantic_integrity_identifier

    RECOMPUTE_WHEN:
      ontology_definition_changes
      relationship_model_changes
      constraint_model_changes
      reasoning_rule_changes
      unit_model_changes
  }

}

END FLOW