Add links — kinematics

symplyphysics/laws/kinematics/angular_momentum_is_rotational_inertia_times_angular_speed.py

@@ -10,6 +10,10 @@
 
 #. The body is rigid.
 #. The axis of rotation is fixed.
+
+**Links:**
+
+#. `Wikipedia, vector counterpart of this law <https://en.wikipedia.org/wiki/Angular_momentum#Orbital_angular_momentum_in_three_dimensions>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/angular_position_is_arc_length_over_radius.py

@@ -6,6 +6,12 @@
 assumed to be fixed in the body, perpendicular to that axis and rotating with the body. The angular
 position of this is measured relative to a fixed direction and is expressed as a ratio of the arc
 length of a circular path and its radius (distance to the axis).
+
+**Links:**
+
+#. `Wikipedia, similar concept <https://en.wikipedia.org/wiki/Central_angle#Formulas>`__.
+
+#. `openstax, table 6.2, first line <https://openstax.org/books/physics/pages/6-3-rotational-motion>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/angular_position_via_constant_angular_acceleration_and_time.py

@@ -6,6 +6,10 @@
 
 #. The axis is fixed.
 #. Angular acceleration is constant, i.e. :math:`\frac{d \alpha}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, second out of the last four equations in the paragraph <https://en.wikipedia.org/wiki/Kinematics#Acceleration_2>`__.
 """
 
 from sympy import Eq, solve, dsolve

symplyphysics/laws/kinematics/angular_position_via_constant_angular_speed_and_time.py

@@ -7,6 +7,10 @@
 
 #. The axis is fixed.
 #. Angular speed is constant, i.e. :math:`\frac{d \omega}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, second out of the last four equations in the paragraph <https://en.wikipedia.org/wiki/Kinematics#Acceleration_2>`__.
 """
 
 from sympy import Eq, solve, dsolve

symplyphysics/laws/kinematics/angular_speed_via_constant_angular_acceleration_and_time.py

@@ -9,6 +9,10 @@
 
 #. The axis is fixed.
 #. Angular acceleration is constant, i.e. :math:`\frac{d \alpha}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, first out of the last four equations in the paragraph <https://en.wikipedia.org/wiki/Kinematics#Acceleration_2>`__.
 """
 
 from sympy import Eq, dsolve, solve

symplyphysics/laws/kinematics/average_angular_speed_is_angular_distance_over_time.py

@@ -4,6 +4,10 @@
 
 *Angular speed*, or *angular frequency*, is a scalar physical quantity measuring
 the rate of change in angle of rotation over time.
+
+**Links:**
+
+#. `BYJU's <https://byjus.com/physics/angular-velocity/#average-angular-velocity>`__.
 """
 
 from sympy import (Eq, solve)

symplyphysics/laws/kinematics/centripetal_acceleration_via_angular_speed_and_radius.py

@@ -3,6 +3,10 @@
 =====================================================
 
 *Centripetal acceleration* is defined as the change in velocity tangential to the velocity vector.
+
+**Links:**
+
+#. `Physics LibreTexts, second part of equation 6.2.5 <https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/06%3A_Uniform_Circular_Motion_and_Gravitation/6.02%3A_Centripetal_Acceleration>`__.
 """
 
 from sympy import Eq, solve

symplyphysics/laws/kinematics/centripetal_acceleration_via_linear_speed_and_radius.py

@@ -3,6 +3,10 @@
 ====================================================
 
 *Centripetal acceleration* is defined as the change in velocity tangential to the velocity vector.
+
+**Links:**
+
+#. `Physics LibreTexts, first part of equation 6.2.5 <https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/06%3A_Uniform_Circular_Motion_and_Gravitation/6.02%3A_Centripetal_Acceleration>`__.
 """
 
 from sympy import Eq, solve, sin, cos, Derivative, pi

symplyphysics/laws/kinematics/classical_addition_of_velocities.py

@@ -12,6 +12,10 @@
 #. Velocity vectors must be collinear.
 #. Space and time are absolute.
 #. Applicable to inertial reference frames.
+
+**Links:**
+
+#. `Wikipedia, vector counterpart of this law <https://en.wikipedia.org/wiki/Velocity-addition_formula#Galilean_relativity>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/displacement_in_simple_harmonic_motion.py

@@ -10,6 +10,10 @@
 
 #. This law is also applicable for any physical quantity that changes its value in
    a repeating harmonic manner, therefore :symbols:`any_quantity` is used.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Simple_harmonic_motion#Dynamics>`__.
 """
 
 from sympy import Eq, cos, dsolve

symplyphysics/laws/kinematics/position_via_constant_acceleration_and_time.py

@@ -7,6 +7,10 @@
 **Conditions:**
 
 #. Acceleration is constant, i.e. :math:`\frac{d a}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, vector counterpart of this law <https://en.wikipedia.org/wiki/Kinematics#Relative_acceleration>`__.
 """
 
 from sympy import Eq, solve, dsolve

symplyphysics/laws/kinematics/position_via_constant_speed_and_time.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. Speed is constant, i.e. :math:`\frac{d v}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, derivable from the vector counterpart of this law <https://en.wikipedia.org/wiki/Kinematics#Relative_acceleration>`__.
 """
 
 from sympy import (Eq, solve, dsolve)

symplyphysics/laws/kinematics/rotational_inertia/geometries/slab_about_perpendicular_axis_through_center.py

@@ -7,6 +7,10 @@
 **Conditions:**
 
 #. The slab is uniform.
+
+**Links:**
+
+#. `Wikipedia, see table <https://en.wikipedia.org/wiki/List_of_moments_of_inertia>`__.
 """
 
 from sympy import Eq, sqrt

symplyphysics/laws/kinematics/rotational_inertia/geometries/solid_disk_about_central_axis.py

@@ -7,6 +7,10 @@
 **Conditions:**
 
 #. The disk is uniform.
+
+**Links:**
+
+#. `Wikipedia, sixth row of table <https://en.wikipedia.org/wiki/List_of_moments_of_inertia>`__.
 """
 
 from sympy import Eq, pi

symplyphysics/laws/kinematics/rotational_inertia/geometries/thin_rod_about_axis_through_center_perpendicular_to_length.py

@@ -8,6 +8,10 @@
 
 #. The rod is uniform.
 #. The rod is thin, i.e. its diameter is much less than its length.
+
+**Links:**
+
+#. `Wikipedia, third row of table <https://en.wikipedia.org/wiki/List_of_moments_of_inertia>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/rotational_inertia/rotational_inertia_about_axis_and_through_center_of_mass.py

@@ -6,11 +6,14 @@
 that of the same body about a parallel axis that extends through the body's center of mass
 of mass).
 
-
 **Conditions:**
 
 #. The two axes must be parallel to each other.
 #. The axis used in the calculation of :math:`I_\text{com}` must pass through the body's center of mass.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Parallel_axis_theorem#Mass_moment_of_inertia>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/rotational_inertia/rotational_inertia_cartesian_integral.py

@@ -23,6 +23,9 @@
 # Note:
 ## - The integration is carried out over the entire body as to include every volume element.
 
+# Links:
+## Wikipedia, derivable from fourth equation <https://en.wikipedia.org/wiki/Moment_of_inertia#Point_mass>
+
 rotational_inertia = Symbol("rotational_inertia", units.mass * units.length**2)
 density = Function("density", units.mass / units.length**3)
 distance_to_axis = Function("distance_to_axis", units.length)

symplyphysics/laws/kinematics/rotational_inertia/rotational_inertia_cylindrical_integral.py

@@ -22,7 +22,10 @@
 
 # Notes:
 ## - The integration is carried out over the entire body as to include every volume element.
-## - THe z-axis is the rotational axis of the body
+## - The z-axis is the rotational axis of the body
+
+# Links:
+## Wikipedia, derivable from fourth equation <https://en.wikipedia.org/wiki/Moment_of_inertia#Point_mass>
 
 rotational_inertia = Symbol("rotational_inertia", units.mass * units.length**2)
 density = Function("density", units.mass / units.length**3)

symplyphysics/laws/kinematics/rotational_inertia/rotational_inertia_is_additive.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. The rotational inertia is calculated for the same axis for all parts of the system.
+
+**Links:**
+
+#. `Wikipedia, see second paragraph <https://en.wikipedia.org/wiki/Moment_of_inertia>`__.
 """
 
 from typing import Sequence

symplyphysics/laws/kinematics/rotational_inertia/rotational_inertia_of_particle.py

@@ -4,6 +4,10 @@
 
 Rotational inertia of a rotating particle is defined as the product of its mass
 and the squared radius of rotation.
+
+**Links:**
+
+#. `Wikipedia, third equation <https://en.wikipedia.org/wiki/Moment_of_inertia#Definition>`__.
 """
 
 from sympy import Eq

symplyphysics/laws/kinematics/speed_via_angular_speed_and_radius.py

@@ -4,6 +4,10 @@
 
 Speed of a rotating body can be calculated using its angular speed and instantaneous
 radius of curvature of the body's path.
+
+**Links:**
+
+#. `Physics LibreTexts, first part of formula 6.1.9 <https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/06%3A_Uniform_Circular_Motion_and_Gravitation/6.01%3A_Rotation_Angle_and_Angular_Velocity>`__.
 """
 
 from sympy import Eq, solve

symplyphysics/laws/kinematics/speed_via_constant_acceleration_and_time.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. Acceleration is constant, i.e. :math:`\frac{d a}{d t} = 0.`
+
+**Links:**
+
+#. `Wikipedia, vector counterpart of this law <https://en.wikipedia.org/wiki/Kinematics#Relative_acceleration>`__.
 """
 
 from sympy import (Eq, solve)

symplyphysics/laws/kinematics/tangential_acceleration_via_angular_acceleration_and_radius.py

@@ -8,6 +8,10 @@
 **Conditions:**
 
 #. Radius is constant, i.e. :math:`\frac{d r}{d t} = 0.`
+
+**Links:**
+
+#. Equation 10-22 on p. 269 of "Fundamentals of Physics" by David Halladay et al., 10th Ed.
 """
 
 from sympy import Eq, solve, Derivative

symplyphysics/laws/kinematics/vector/absolute_velocity_of_arbitrary_motion.py

@@ -10,6 +10,13 @@
 **Notes:**
 
 #. Moving frame :math:`S'` can perform both translational and rotational motion.
+
+**Links:**
+
+#. `Wikipedia <https://ru.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5#%D0%A1%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C>`__.
+
+..
+    TODO: find English link
 """
 
 from symplyphysics import (

symplyphysics/laws/kinematics/vector/acceleration_due_to_non_uniform_rotation.py

@@ -9,6 +9,13 @@
 **Notation:**
 
 #. :math:`\vec a \times \vec b` (:code:`cross(a, b)`) is vector product of :math:`\vec a` and :math:`\vec b`.
+
+**Links:**
+
+#. `Wikipedia <https://ru.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5#%D0%A3%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B5>`__.
+
+..
+    TODO find English link
 """
 
 from sympy import Expr, abc

symplyphysics/laws/kinematics/vector/acceleration_is_normal_plus_tangential_acceleration.py

@@ -8,6 +8,12 @@
    and points to the instantaneous axis of rotation,
 #. and *tangential acceleration*, which is responsible for the change in the magnitude of
    the velocity vector.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Circular_motion#Formula>`__.
+
+#. `Mathematica LibreTexts <https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/2%3A_Vector-Valued_Functions_and_Motion_in_Space/2.6%3A_Tangential_and_Normal_Components_of_Acceleration>`__.
 """
 
 from pytest import approx

symplyphysics/laws/kinematics/vector/acceleration_of_transfer_between_relative_frames.py

@@ -9,6 +9,13 @@
 rotation of the moving frame. The transfer acceleration only depends on the motion of frame :math:`S'` relative to
 stationary frame :math:`S`, so its physical meaning would be that it is the acceleration in :math:`S` of a point stationary
 in :math:`S'`.
+
+**Links:**
+
+#. `Wikipedia <https://ru.wikipedia.org/wiki/%D0%A1%D0%BB%D0%BE%D0%B6%D0%BD%D0%BE%D0%B5_%D0%B4%D0%B2%D0%B8%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5#%D0%A3%D1%81%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D0%B8%D0%B5>`__.
+
+..
+    TODO find English link
 """
 
 from symplyphysics import (

symplyphysics/laws/kinematics/vector/center_of_mass_for_system_of_particles.py

@@ -4,6 +4,10 @@
 
 The center of mass (com) of a system of particles is a unique point at any given time where
 the sum of weighted relative positions of the distributed mass is zero.
+
+**Links:**
+
+#. `Wikipedia, second formula <https://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles>`__.
 """
 
 from typing import Sequence

symplyphysics/laws/kinematics/vector/centrifugal_acceleration_via_centripetal_acceleration.py

@@ -4,6 +4,10 @@
 
 The vector of *centrifugal acceleration* has the same magnitude as the vector of *centripetal
 acceleration* but is directed oppositely to it.
+
+**Links:**
+
+#. `BYJU's <https://byjus.com/physics/centripetal-and-centrifugal-force/>`__.
 """
 
 from symplyphysics import (

symplyphysics/laws/kinematics/vector/centripetal_acceleration_via_cross_product.py

@@ -10,6 +10,10 @@
 **Notation:**
 
 #. :math:`\vec a \times \vec b` (:code:`cross(a, b)`) is the cross product between :math:`\vec a` and :math:`\vec b`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Centripetal_force#Derivation_using_vectors>`__.
 """
 
 from sympy import symbols

symplyphysics/laws/kinematics/vector/centripetal_acceleration_via_vector_rejection.py

@@ -13,6 +13,10 @@
 #. :math:`\text{oproj}_{\vec b} \vec a` (:code:`reject(a, b)`) is the rejection of
    :math:`\vec a` from :math:`\vec b`, i.e. the component of :math:`\vec a` orthogonal
    to :math:`\vec b`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Centripetal_force#Derivation_using_vectors>`__.
 """
 
 from symplyphysics import (

symplyphysics/laws/kinematics/vector/coriolis_acceleration.py

@@ -10,6 +10,10 @@
 Suppose a reference frame :math:`S'` is fixed to a rotating body :math:`A` (e.g. Earth), so that frame :math:`S'` rotates w.r.t.
 another static reference frame :math:`S`. The Coriolis acceleration is the acceleration another body :math:`B` has when
 moving within rotating reference frame :math:`S'`, so it is essentially zero for objects at rest in :math:`S'`.
+
+**Links:**
+
+#. `Wikipedia <https://en.wikipedia.org/wiki/Coriolis_force#Formula>`__.
 """
 
 from symplyphysics import (

symplyphysics/laws/kinematics/vector/displacement_is_angular_displacement_cross_radius.py

@@ -9,6 +9,10 @@
 
 #. The axis is fixed.
 #. Angular displacement pseudovector and radius vector must be orthogonal to one another.
+
+**Links:**
+
+#. `Physics LibreTexts, formula 11.1.4 <https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/11%3A_Rotational_dynamics/11.01%3A_Rotational_kinematic_vectors>`__.
 """
 
 from pytest import approx

symplyphysics/laws/kinematics/vector/velocity_of_transfer_between_reference_frames.py

@@ -24,6 +24,9 @@
 ## w - pseudovector of angular velocity related to rotation of moving frame S' about instantaneous axis
 ## r - vector of position of point X relative to moving frame S'
 
+# Links: Wikipedia, first formula <https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC%D0%B0_%D0%BE_%D1%81%D0%BB%D0%BE%D0%B6%D0%B5%D0%BD%D0%B8%D0%B8_%D1%81%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D0%B5%D0%B9#%D0%9E%D0%B1%D1%81%D1%83%D0%B6%D0%B4%D0%B5%D0%BD%D0%B8%D0%B5>
+# TODO: find English link
+
 
 def transfer_velocity_law(
     moving_frame_velocity_: Vector,