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Theorem in planar dynamics
The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem, named after Christiaan Huygens and Jakob Steiner, can be
Parallel_axis_theorem
Mathematical theorem
perpendicular axis theorem states that I z = I x + I y {\displaystyle I_{z}=I_{x}+I_{y}} This rule can be applied with the parallel axis theorem and the stretch
Perpendicular_axis_theorem
Mathematical construct in engineering
centroidal axis, x {\displaystyle x} , and use the parallel axis theorem to derive the second moment of area with respect to the x ′ {\displaystyle x'} axis. The
Second_moment_of_area
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
{\displaystyle L} is the length of the pendulum. Notice that the parallel axis theorem is used to shift the moment of inertia from the center of mass to
Moment_of_inertia
_{A}x^{2}\,dx\,dy.} The parallel axis theorem can be used to determine the second moment of area of a rigid body about any axis, given the body's second
List of second moments of area
List_of_second_moments_of_area
Type of motion which combines translation and rotation with respect to a surface
object mass and velocity, the above result may be used with the parallel axis theorem to obtain the kinetic energy associated with simple rolling K rolling
Rolling
Every rigid motion is a screw displacement
components, one parallel to the axis of rotation associated with the isometry and the other component perpendicular to that axis. The Chasles theorem states that
Chasles'_theorem_(kinematics)
On the existence of hyperplanes separating disjoint convex sets
the theorem, if both these sets are closed and at least one of them is compact, then there is a hyperplane in between them and even two parallel hyperplanes
Hyperplane_separation_theorem
Moment of inertia of diff geometric shapes
remember that it is an additive function and exploit the parallel axis and the perpendicular axis theorems. This article considers mainly symmetric mass distributions
List_of_moments_of_inertia
König's theorem (physics) Lami's theorem (statics) Liouville's theorem (Hamiltonian mechanics) Parallel axis theorem (physics) Perpendicular axis theorem (physics)
List_of_theorems
Fundamental principle of classical physics
Newton's laws of motion Classical mechanics Special relativity Parallel axis theorem Britannica, Dictionary. "definition of INERTIA". Retrieved 2022-07-08
Inertia
Theorem in projective geometry
lists various exceptions involving parallel lines. Desargues's theorem is therefore one of the simplest geometric theorems whose natural home is in projective
Desargues's_theorem
Structural element capable of withstanding loads by resisting bending
construction. Because of the parallel axis theorem and the fact that most of the material is away from the neutral axis, the second moment of area of
Beam_(structure)
Universality of construction using just a straightedge and a single circle with center
In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states
Poncelet–Steiner_theorem
Topics referred to by the same term
Steiner, Mississippi, U.S. Steiner's theorem, or parallel axis theorem Steiner tree Poncelet–Steiner theorem Steiner surface Steiner system, a type
Steiner
Classical mechanics rule
the axis. This operation leaves cylinders oriented parallel to the axis unchanged in radius. This rule can be applied with the parallel axis theorem and
Stretch_rule
Movement with a fixed point is rotation
The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically
Euler's_rotation_theorem
Theorem in mathematics
In mathematics, the projection-slice theorem, central slice theorem or Fourier slice theorem in two dimensions states that the results of the following
Projection-slice_theorem
Energy of a moving physical body
Kinetic energy per unit mass of projectiles Kinetic projectile Parallel axis theorem Potential energy Recoil Jain, Mahesh C. (2009). Textbook of Engineering
Kinetic_energy
Type of pendulum
total moment of inertia of Arm 1 about the pivot point (using the parallel axis theorem) is J 1 ^ = J 1 + m 1 l 1 2 {\displaystyle {\hat {J_{1}}}=J_{1}+m_{1}l_{1}^{2}}
Furuta_pendulum
Movement of an object which leaves at least one point unchanged
relative orientation over time. By Euler's theorem, any change in orientation can be described by rotation about an axis through a chosen reference point. Hence
Rotation
Plane curve: conic section
source at the focus is reflected into a parallel ("collimated") beam, leaving the parabola parallel to the axis of symmetry. The same effects occur with
Parabola
{\displaystyle \Omega } , the fluid velocity will be uniform along any line parallel to the axis of rotation. Ω {\displaystyle \Omega } must be large compared to
Taylor–Proudman_theorem
Term in geometry
as the axis of perspectivity, perspective axis, homology axis, or archaically, perspectrix. The figures are said to be perspective from this axis. The point
Perspective_(geometry)
Symmetry-based invariance to continuous group action
example translation parallel to the x-axis by u units, as u varies, is a one-parameter group of motions. Rotation around the z-axis is also a one-parameter
Continuous_symmetry
Geometric axis of rotation and translation
translation of a body occurs. Chasles' theorem shows that each Euclidean displacement in three-dimensional space has a screw axis, and the displacement can be decomposed
Screw_axis
Mathematical theorem
In complex analysis, the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number
Riemann_mapping_theorem
Point where the derivative of a function is zero or undefined (in certain cases)
curve is parallel to the y-axis, and that, at this point, g does not define an implicit function from x to y (see implicit function theorem). If (x0,
Critical_point_(mathematics)
List of definitions of terms and concepts commonly used in aerospace engineering
vectors (position and velocity). Parallel axis theorem – also known as Huygens–Steiner theorem, or just as Steiner's theorem, named after Christiaan Huygens
Glossary of aerospace engineering
Glossary_of_aerospace_engineering
Paraelectricity Parafoil Paraformer Parallax barrier Parallel Worlds (book) Parallel axis theorem Parallelogram of force Paramagnetism Parameterized post-Newtonian
Index_of_physics_articles_(P)
Process of creating equivalent circuits
impedances. There is also a dual Miller theorem with regards to impedance supplied by two current sources connected in parallel. The two versions are based on
Miller_theorem
Sufficiency theorem for reconstructing signals from samples
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals
Nyquist–Shannon sampling theorem
Nyquist–Shannon_sampling_theorem
Theorem about hexagons and conics
Brianchon's theorem has exceptions in the affine plane but not in the projective plane. Brianchon's theorem can be proved by the idea of radical axis or reciprocation
Brianchon's_theorem
Coordinate system using perpendicular axes
each axis. In that case, each coordinate is obtained by projecting the point onto one axis along a direction that is parallel to the other axis (or, in
Cartesian_coordinate_system
Plane curve
{\displaystyle A} that is parallel to the minor axis and a line through B {\displaystyle B} that is parallel to the major axis. These lines meet at an ellipse
Ellipse
Mathematical result in convex functions theory
tangency points for the maximally separated parallel tangents. Legendre transformation Convex conjugate Moreau's theorem Wolfe duality Werner Fenchel Borwein
Fenchel's_duality_theorem
Conic sections with the same foci
determine two pencils of confocal ellipses and hyperbolas. By the principal axis theorem, the plane admits a Cartesian coordinate system with its origin at the
Confocal_conic_sections
Curve where spinning and moving lines cross
of squaring the circle, hence its name as a quadratrix. Dinostratus's theorem, used by Dinostratus to square the circle, relates an endpoint of the curve
Quadratrix_of_Hippias
Planar maps require at most four colors
In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map
Four_color_theorem
Equation for radii of tangent circles
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic
Descartes'_theorem
Plane curve: conic section
= a 2 c {\textstyle d={\frac {a^{2}}{c}}} from the center and parallel to the minor axis are called directrices of the hyperbola (see diagram). For an
Hyperbola
Polygon in which all angles are right
rectilinear polygon is an axis-aligned rectangle - a rectangle with 2 sides parallel to the x axis and 2 sides parallel to the y axis. See also: Minimum bounding
Rectilinear_polygon
Relationship between two lines that meet at a right angle
axis. To make the perpendicular to the line g at or through the point P using Thales's theorem, see the animation at right. The Pythagorean theorem can
Perpendicular
Surface created by rotating a curve about an axis
cylindrical and conical surfaces depending on whether or not the line is parallel to the axis. A circle that is rotated around any diameter generates a sphere
Surface_of_revolution
Graph invariant defined from axis-parallel unit cubes
dimension such that a graph can be realized as the intersection graph of axis-parallel unit cubes in Euclidean space. Cubicity was introduced by Fred S. Roberts
Cubicity
Artistic concept relating to perspective
therefore lines parallel to these axes intersect, resulting in three different vanishing points. The vanishing point theorem is the principal theorem in the science
Vanishing_point
Description of flat one-vertex origami
Kawasaki's theorem or Kawasaki–Justin theorem is a theorem in the mathematics of paper folding that describes the crease patterns with a single vertex
Kawasaki's_theorem
Type of technical drawing
perspective, one face of the projected object is parallel to the viewing plane, and the third axis is projected as going off at an angle (typically atan(2)
Oblique_projection
In differential geometry Dupin's theorem, named after the French mathematician Charles Dupin, is the statement: The intersection curve of any pair of
Dupin's_theorem
Method for visually representing three-dimensional objects
to the middle of any edge as √2 using Pythagoras' theorem . By rotating the cube by 45° on the x-axis, the point (1, 1, 1) will therefore become (1, 0
Isometric_projection
Simple curve of Euclidean geometry
stereographic projection of the line passing through the centre parallel to the x axis (see Tangent half-angle substitution). However, this parameterisation
Circle
Quadrilateral with four right angles
both right-angled rectangles and crossed rectangles. Each has an axis of symmetry parallel to and equidistant from a pair of opposite sides, and another
Rectangle
Quantity of resistance to torsional deformation
constituent of the second moment of area, linked through the perpendicular axis theorem. Where the planar second moment of area describes an object's resistance
Second_polar_moment_of_area
Intrinsic quantum property of particles
{\displaystyle e^{iS\theta }\ ,} for rotation of angle θ around the axis parallel to the spin S. This is equivalent to the quantum-mechanical interpretation
Spin_(physics)
Operation in mathematical calculus
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides
Integral
Type of motion
instantaneous axis of rotation changing its orientation and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous
Rotation_around_a_fixed_axis
Type of three-dimensional shape
slice that was drawn is perpendicular to the axis of revolution; i.e. when integrating parallel to the axis of revolution. The volume of the solid formed
Solid_of_revolution
Polyhedron in which all edges are parallel
between Jessen's icosahedron's faces are right angles, the edges are not axis-parallel, thus Jessen's icosahedron is not an orthogonal polyhedron. Polycubes
Orthogonal_polyhedron
Type of geometric transformation
in the opposite direction, while points on the axis stay fixed. Straight lines parallel to the x-axis remain where they are, while all other lines are
Shear_mapping
Overview of and topical guide to geometry
Miniver's problem Isoperimetric theorem Annulus Ptolemaios' theorem Steiner chain Eccentricity Ellipse Semi-major axis Hyperbola Parabola Matrix representation
Outline_of_geometry
Curve from a cone intersecting a plane
plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the
Conic_section
Fluid flow revolving around an axis of rotation
axis of rotation. The axis itself is one of the vortex lines, a limiting case of a vortex tube with zero diameter. According to Helmholtz's theorems,
Vortex
Quadric surface that looks like a deformed sphere
whose axis of rotation is the tangent line of the hyperbola at V. If one allows the center V to disappear into infinity, one gets an orthogonal parallel projection
Ellipsoid
Point from which two similar geometric figures can be scaled to each other
two circles are the solution. Intercept theorem Similarity (geometry) Homothetic transformation Radical axis, radical center Apollonius' problem Weisstein
Homothetic_center
Pseudovector field describing the local rotation of a continuum near some point
travel parallel to the axis of the pipe; but faster near that axis, and practically stationary next to the walls. The vorticity will be zero on the axis, and
Vorticity
Straight figure with zero width and depth
set of complex numbers. Affine transformation Coordinate axis Curve Distance between two parallel lines Distance from a point to a line Flat (geometry) Incidence
Line_(geometry)
Mathematical treatise by Archimedes
The Method of Mechanical Theorems (Greek: Περὶ μηχανικῶν θεωρημάτων πρὸς Ἐρατοσθένη ἔφοδος), also referred to as The Method, is one of the major surviving
The Method of Mechanical Theorems
The_Method_of_Mechanical_Theorems
Mathematical formulation of vector pairs used in physics (rigid body dynamics)
screws; Chasles' theorem proves that any change between two rigid object poses can be performed by a single screw; the intermediate axis theorem proves that
Screw_theory
Property of objects which appear unchanged after a partial rotation
Axial symmetry Crystallographic restriction theorem Lorentz symmetry Point groups in three dimensions Screw axis Space group Translational symmetry Rotational
Rotational_symmetry
Mathematical theorem
for the symmetry to hold are given by Schwarz's theorem, also called Clairaut's theorem or Young's theorem. In the context of partial differential equations
Symmetry of second derivatives
Symmetry_of_second_derivatives
Method for calculating the volume of a solid of revolution
along an axis perpendicular to the axis of revolution. This is in contrast to disc integration which integrates along the axis parallel to the axis of revolution
Shell_integration
Surface of revolution with a hole in the middle
The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to
Toroid
Fluid dynamics phenomenon due to the Coriolis effect
solid body tend to form columns parallel to the axis of rotation called Taylor columns. An object moving parallel to the axis of rotation in a rotating fluid
Taylor_column
Formula in classical differential geometry
183 Pressley (p. 185) explains this theorem as an expression of conservation of angular momentum about the axis of revolution when a particle moves along
Clairaut's relation (differential geometry)
Clairaut's_relation_(differential_geometry)
Mathematical analysis technique
is the bias (distance). This is a statistical application of the parallel-axis theorem from mechanics. In summary, the linearized approximation for the
Experimental uncertainty analysis
Experimental_uncertainty_analysis
Integral transform used in various branches of mathematics
that the limits of integration are ±∞, and all lines of sight are parallel to the x axis. Realizing that the radius r is related to x and y as r2 = x2 +
Abel_transform
Equivalence under a change of basis (linear algebra)
original and transformed vectors in a new basis containing a vector parallel to the axis of rotation. In the original basis, the transform would be written
Matrix_similarity
Tool for measuring area
moves perpendicular to its axis, it rolls, and this movement is recorded. When the measuring wheel moves parallel to its axis, the wheel skids without rolling
Planimeter
Straight line segment that passes through the centre of a circle
diameters are called the major axis and minor axis, respectively. Conjugate diameters are a pair of diameters where one is parallel to a tangent to the ellipse
Diameter
Geometrical concept
cylinder's axis of symmetry, or an ellipse if it is neither parallel nor perpendicular to that axis. If the cutting plane is parallel to the axis the plane
Cross_section_(geometry)
Polygon with four crossed edges of two lengths
pairs of equal-length sides, but these pairs of sides are not in general parallel. Instead, each pair of sides is antiparallel with respect to the other
Antiparallelogram
Geometric figure which has infinite surface area but finite volume
{\displaystyle {\sqrt {2}}} : Theorem. An acute hyperbolic solid, infinitely long, cut by a plane [perpendicular] to the axis, together with the cylinder
Gabriel's_horn
Isomorphism of projective spaces in geometry
general, some collineations are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective
Homography
Euclidean geometry without distance and angles
are parallel and the lines BC' and B'C are parallel, then the lines CA' and C'A are parallel. (This is the affine version of Pappus's hexagon theorem).
Affine_geometry
Shape with four equal sides and angles
rigid transformations of the plane take the square to itself: For an axis-parallel square centered at the origin, each symmetry acts by a combination of
Square
Theory of irregularities of distribution
Beck–Fiala theorem Six Standard Deviations Suffice (Spencer) The unsolved problems relating to discrepancy theory include: Axis-parallel rectangles in
Discrepancy_theory
Manifold that "locally looks like" Euclidean space
complete flat manifold is Euclidean space. This can be used to prove the theorem of Bieberbach (1911, 1912) that all compact flat manifolds are finitely
Flat_manifold
Geometric model of the physical space
(apex) the point of intersection. However, if the generatrix and axis are parallel, then the surface of revolution is a circular cylinder. In analogy
Three-dimensional_space
parallel to L rather than arc length itself. This method is well suited to computation of the area of an arbitrary polygon. Taking L to be the x-axis
Area_of_a_triangle
2nd-degree plane curve which is reducible
cone or when the cone degenerates to a cylinder and the plane is parallel to the axis of the cylinder. See Conic section#Degenerate cases for details.
Degenerate_conic
Foundational law of electromagnetism relating electric field and charge distributions
as Gauss's flux theorem or sometimes Gauss's theorem, is one of Maxwell's equations. It is an application of the divergence theorem, and it relates the
Gauss's_law
uniformization theorem, that every such surface is conformally equivalent to either the Riemann sphere or the complex plane with slits parallel to the real axis removed
Planar_Riemann_surface
Line which touches a circle at exactly one point
circle's interior. Tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs
Tangent_lines_to_circles
Tool for solving polynomial equations
rightmost point). Then, starting at P0, draw a ray straight down parallel with the y-axis, and rotate this ray counter-clockwise until it hits the point
Newton_polygon
Integration method to calculate volume
revolution of a solid-state material when integrating along an axis parallel to the axis of revolution. This method models the resulting three-dimensional
Disc_integration
Concept in 3-dimensional geometry
the plane normal ^n and the z-axis. Bivector, representing an oriented area in any number of dimensions De Gua's theorem, on the decomposition of vector
Vector_area
Method for characterising the local shape of a surface
a method for characterising the local shape of a surface. Draw a plane parallel to the tangent plane and a small distance away from it. Consider the intersection
Dupin_indicatrix
Mechanism by which materials form into and are attracted to magnets
its ferromagnetic state, PuP's easy axis is in the ⟨100⟩ direction.[relevant? – discuss] In NpFe2 the easy axis is ⟨111⟩. Above TC ≈ 500 K, NpFe2 is
Ferromagnetism
Type of non-Euclidean geometry
the parallel postulate is not provable from the other postulates), but their efforts led to the discovery of hyperbolic geometry. The theorems of Alhacen
Hyperbolic_geometry
Direction and rate of rotation
26 rad/h) and angular velocity direction (a unit vector) parallel to Earth's rotation axis ( ω ^ = Z ^ {\displaystyle {\hat {\omega }}={\hat {Z}}}
Angular_velocity
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
Girl/Female
Assamese, Indian
Tall; Pivot; Pole; Axis
Boy/Male
Shakespearean
All's Well That Ends Well.' A follower of Bertram, Count of Rousillon.
Boy/Male
Arabic, Muslim
Pivot; Pole; Axis; Celebrity; Personality
Female
English
 English adopted use of German Avis ("refuge in war"). But its popularity in the Middle Ages was due to its association with the Latin noun avis, AVIS means "bird."Â
Female
German
 Old German nickname, possibly AVIS means "refuge in war." Compare with another form of Avis.
Surname or Lastname
English
English : variant of Ames.
Female
English
 Short form of English Alisa, ALIS means "noble sort." Compare with another form of Alis.
Boy/Male
Egyptian
Apis.
Female
Welsh
 Welsh form of French Alais, ALIS means "noble sort." Compare with another form of Alis.
Girl/Female
Biblical
Parables, governing.
Girl/Female
Indian
Axis
Male
Egyptian
, Apis.
Boy/Male
Indian, Sanskrit
Axis; Yoke
Biblical
parables; governing
Boy/Male
Indian
Close friend, Good company, Smart one, Companion, Supreme
Boy/Male
Muslim
Pivot. Pole. Axis. Celebrity.
Girl/Female
Indian
Blessing, Prayer
Boy/Male
Egyptian
Mythical dead bull thought to be Osiris.
Boy/Male
Muslim
Pivot. Pole. Axis. Celebrity.
Surname or Lastname
English
English : from the Norman female personal name Avice (Old French Avice, Latin Avitia, also found in a masculine form, Avitius). This is of uncertain origin, perhaps from a Celtic (Gaulish) name.French : Tanguay and Jetté have people named Avice, Avisse in Quebec from 1666. Nègre has an Avèze (Puy-de-Dome) also deriving from Avitius.
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
Girl/Female
Muslim
Sister
Girl/Female
Arabic, Muslim
Inseparable Friend
Boy/Male
Tamil
Killan | கிலà¯à®²à®¾à®¨
Female
Egyptian
, a form of Muts-netem.
Girl/Female
American, Australian
Female Version of Daniel
Boy/Male
Hindu, Indian, Traditional
Glory of God
Boy/Male
Native American
Little wolf.
Boy/Male
Arabic, Muslim
Beauty of the Religion (Islam)
Girl/Female
Latin
Sister of Daedalus.
Boy/Male
English
Hiding place; hidden area.
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
PARALLEL AXIS-THEOREM
n.
A character consisting of two parallel vertical lines (thus, ) used in the text to direct attention to a similarly marked note in the margin or at the foot of a page.
n.
A line which, throughout its whole extent, is equidistant from another line; a parallel line, a parallel plane, etc.
n.
A comparison made; elaborate tracing of similarity; as, Johnson's parallel between Dryden and Pope.
imp. & p. p.
of Parallel
a.
Having opposite surfaces exactly plane and parallel, as a piece of glass.
v. t.
To produce or adduce as a parallel.
n.
One of the imaginary circles on the surface of the earth, parallel to the equator, marking the latitude; also, the corresponding line on a globe or map.
n.
A plane parallel to two of the crystalline axes.
a.
Cleaving in more directions than one, parallel to the axis.
n.
A straight line with respect to which the different parts of a magnitude are symmetrically arranged; as, the axis of a cylinder, i. e., the axis of a cone, that is, the straight line joining the vertex and the center of the base; the axis of a circle, any straight line passing through the center.
n.
The space between two axes. See Axis, 6.
v. t.
To represent by parable.
adv.
In a parallel manner; with parallelism.
pl.
of Axis
n.
A dome parallel to the shorter lateral axis. See Dome.
n.
The spotted deer (Cervus axis or Axis maculata) of India, where it is called hog deer and parrah (Moorish name).
v. i.
To be parallel; to correspond; to be like.
v. t.
To place or set so as to be parallel; to place so as to be parallel to, or to conform in direction with, something else.
a.
Extended in the same direction, and in all parts equally distant; as, parallel lines; parallel planes.
a.
Continuing a resemblance through many particulars; applicable in all essential parts; like; similar; as, a parallel case; a parallel passage.