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Class of radio navigation systems
Hyperbolic navigation is a class of radio navigation systems in which a navigation receiver instrument is used to determine location based on the difference
Hyperbolic_navigation
First global radio navigation system for aircraft
global-range radio navigation system, operated by the United States in cooperation with six partner nations. It was a hyperbolic navigation system, enabling
Omega_(navigation_system)
Skills and tech involved in submarine navigation
global-range radio hyperbolic navigation system, no longer in use Alpha, the Russian counterpart of the Omega Navigation System Celestial navigation using the
Submarine_navigation
Radio navigation system
metres at ranges up to about 350 miles (560 km). It was the first hyperbolic navigation system to be used operationally, entering service with RAF Bomber
Gee_(navigation)
Use of radio-frequency electromagnetic waves to determine position on the Earth's surface
needed] Since the 1960s, navigation has increasingly moved to satellite navigation systems. These are essentially hyperbolic systems whose transmitters
Radio_navigation
Process of monitoring and controlling the movement of a craft or vehicle
OMEGA, and LORAN-C are three similar hyperbolic navigation systems. Decca was a hyperbolic low frequency radio navigation system (also known as multilateration)
Navigation
American satellite-based radio navigation service
satellite-based hyperbolic navigation system owned by the United States Space Force and operated by Mission Delta 31. It is one of the global navigation satellite
Global_Positioning_System
Long-range radio navigation system
E-LORAN, or e-LORAN) is a long-range radio navigation system that uses terrestrial towers and the hyperbolic navigation technique. It is an advancement in receiver
ELoran
Use of distances for determining unknown coordinates of a point
the TOAs are multiple and known. When MLAT is used for navigation (as in hyperbolic navigation), the waves are transmitted by the stations and received
Trilateration
Radio navigation system
LORAN (Long Range Navigation) was a hyperbolic radio navigation system developed in the United States during World War II. It was similar to the UK's
LORAN
Navigation and surveillance technique
the TOAs are multiple and known. When MLAT is used for navigation (as in hyperbolic navigation), the waves are transmitted by the stations and received
Pseudo-range_multilateration
Branch of mathematics
known: the problem is to identify the positions for all sensors. Hyperbolic navigation is one pre-GPS technology that uses distance geometry for locating
Distance_geometry
Radio navigation system
Loran-C is a hyperbolic radio navigation system that allows a receiver to determine its position by listening to low frequency radio signals that are
Loran-C
Estimation of orbits of objects
Network. A satellite trying to determine its own orbit can use a hyperbolic navigation system for the state vectors (location and velocity) as well as
Orbit_determination
World War II radar research organization at the Massachusetts Institute of Technology
Long-range navigation was the last of the three charter projects assigned to the Radiation Laboratory. In October 1940, Alfred Loomis proposed a hyperbolic navigation
MIT_Radiation_Laboratory
Transponder-based navigation system – GEE-H AMES Type 700, 1.7–2.0 MHz Hyperbolic navigation system – LORAN AMES Type 7000, 30–60 MHz Hyperbolic navigation system
Air Ministry Experimental Station
Air_Ministry_Experimental_Station
Radio navigation system for ships and aircraft
The Decca Navigator System was a hyperbolic radio navigation system that allowed ships and aircraft to determine their position by using radio signals
Decca_Navigator_System
Surface-to-surface cruise missile
SHANICLE (Short Range Navigation Vehicle) guidance system. This was essentially an adaptation of the LORAN hyperbolic navigation system to microwave frequencies
MGM-1_Matador
RAF target-marking squadrons in World War II
started development of a number of night navigation aids and were already testing the Gee hyperbolic navigation system on operations. These would be available
Pathfinder_(RAF)
Water layer used in ocean surveillance
the 1962 edition of The American Practical Navigator among the hyperbolic navigation systems. The early applications relied on fixed shore stations,
SOFAR_channel
Curve on the sphere analogous to an ellipse or hyperbola
at a point on an ellipsoid of revolution, the hyperbolae used in hyperbolic navigation (which determines position based on the difference in received signal
Spherical_conic
Event causing a ship to wreck
as radio communication, radar navigation, the gyrocompass, sonar, hyperbolic radio navigation, and satellite navigation Inspection of shipbuilding quality
Shipwrecking
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, exponentials, and
CORDIC
Cylindrical conformal map projection
1569. In the 18th century, it became the standard map projection for navigation due to its property of representing rhumb lines as straight lines. When
Mercator_projection
Radio navigation system developed by Britain during World War II
from Blanchard, W. F. (September 1991). "Air Navigation Systems Chapter 4. Hyperbolic Airborne Radio Navigation Aids – A Navigator's View of their History
Gee-H_(navigation)
Plane curve: conic section
cone Hyperbolic cylinder Hyperbolic paraboloid Hyperboloid of one sheet Hyperboloid of two sheets Elliptic cone Hyperbolic cylinder Hyperbolic paraboloid
Hyperbola
Mathematical function relating circular and hyperbolic functions
In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called
Gudermannian_function
Rational function of the form (az + b)/(cz + d)
orientation-preserving isometries of hyperbolic 3-space and therefore plays an important role when studying hyperbolic 3-manifolds. In physics, the identity
Möbius_transformation
Pioneer Award is selected by the Professional Group on Aeronautical and Navigational Electronics and has been given out annually since 1949. The Pioneer Award
Pioneer_Award_(aviation)
Horizontal angle from north or other reference cardinal direction
to 360° or in the signed range -180° to +180°. The concept is used in navigation, astronomy, engineering, mapping, geodesy, mining, and ballistics. The
Azimuth
Radar field operation of the MIT Radiation Laboratory
reliable navigation to find targets and return safely, particularly at night or through weather. The British Gee system provided hyperbolic navigation using
British Branch of the Radiation Laboratory
British_Branch_of_the_Radiation_Laboratory
Field of classical mechanics concerned with the motion of spacecraft
Leonhard Euler in 1744, whose work was in turn generalised to elliptical and hyperbolic orbits by Johann Lambert in 1761–1777. Another milestone in orbit determination
Orbital_mechanics
velocity. Radial hyperbolic orbit: An open hyperbolic orbit where the object is moving at greater than the escape velocity. This is a hyperbolic orbit with
List_of_orbits
U.S. military training in WWII
countermeasures; identification friend or foe techniques; long-range navigation and hyperbolic navigation techniques; and sonar theory and underwater acoustics. Laboratories
Electronics_Training_Program
Concept in celestial mechanics
than the escape speed at its current distance. In contrast if it is on a hyperbolic trajectory its speed will always be higher than the escape speed at its
Escape_velocity
Radio navigation system
Blanchard, Walter (September 1991). "Air Navigation Systems Chapter 4. Hyperbolic Airborne Radio Navigation Aids – A Navigator's View of their History
Lorenz_beam
Arc crossing all meridians of longitude at the same angle
In navigation, a rhumb line (also rhumb (/rʌm/) or loxodrome) is an arc crossing all meridians of longitude at the same angle. It is a path of constant
Rhumb_line
Projection of a sphere through its center onto a plane
projection of the hyperboloid of two sheets, treated as a model for the hyperbolic plane, is called the Beltrami–Klein model. The gnomonic projection is
Gnomonic_projection
Transmitter station in Stirling, Scotland
DAB services also operate from the site. Decca and Dectra were hyperbolic radio navigation systems. Decca has first developed by UK company Decca Radar
Stirling_Transmitting_Station
Antiderivative of the secant function
for some arguments. An alternative expression in terms of the inverse hyperbolic sine arsinh is numerically well behaved for real arguments | ϕ | < 1 2
Integral of the secant function
Integral_of_the_secant_function
Figure formed by two rays meeting at a common point
{\left|g_{ij}U^{i}U^{j}\right|\left|g_{ij}V^{i}V^{j}\right|}}}.} A hyperbolic angle is an argument of a hyperbolic function just as the circular angle is the argument
Angle
Clock used on ships to aid in navigation
in service as backups to the Loran-C hyperbolic radio navigation system until 1988, when the GPS global navigation satellite system was approved as reliable
Marine_chronometer
Distinguished surfaces of dynamic trajectories
usually referred to as hyperbolic LCSs, as they provide a finite-time generalization of the classic concept of normally hyperbolic invariant manifolds in
Lagrangian_coherent_structure
Concept in celestial mechanics
parabolic trajectories rv2 is constant and equal to 2μ. For elliptic and hyperbolic orbits magnitude of μ = 2 times the magnitude of a times the magnitude
Standard gravitational parameter
Standard_gravitational_parameter
Branch of mathematics
between points in the Euclidean plane, while the hyperbolic metric measures the distance in the hyperbolic plane. Other important examples of metrics include
Geometry
Locus of the zeros of a polynomial of degree two
ellipsoids and hyperboloids are special limiting cases. Any real ellipsoid or hyperbolic and be expressed as a repositioned matrix of the form M = P T M ´ P =
Quadric
Radio navigation system
"Air Navigation Systems: Hyperbolic Airborne Radio Navigation Aids – A Navigator's View of their History and Development". The Journal of Navigation. 44
Sonne_(navigation)
Development of the mathematical function
{\displaystyle A(tu)=A(t)+A(u).} At first the reaction to Saint-Vincent's hyperbolic logarithm was a continuation of studies of quadrature as in Christiaan
History_of_logarithms
Inverse functions of sin, cos, tan, etc.
z} , the definitions allow for hyperbolic angles as outputs and can be used to further define the inverse hyperbolic functions. It's possible to algebraically
Inverse trigonometric functions
Inverse_trigonometric_functions
Functions of an angle
functions has a corresponding inverse function and has an analog among the hyperbolic functions. The oldest definitions of trigonometric functions, related
Trigonometric_functions
Table of positions of astronomical objects at given times
In astronomy and celestial navigation, an ephemeris (/ɪˈfɛmərɪs/; pl. ephemerides /ˌɛfəˈmɛrɪˌdiːz/; from Latin ephemeris 'diary', from Ancient Greek ἐφημερίς
Ephemeris
3–30 kHz range of the electromagnetic spectrum
during the 20th century the VLF band was used for long range hyperbolic radio navigation systems which allowed ships and aircraft to determine their geographical
Very_low_frequency
Circular orbit above Earth's Equator and following the direction of Earth's rotation
placed in this orbit for real-time monitoring and data collection, as are navigation satellites in order to provide a known calibration point and enhance GPS
Geostationary_orbit
Swiss watch manufacturer
in service as backups to the Loran-C hyperbolic radio navigation system until 1988 when the GPS global navigation satellite system was approved as reliable
Hamilton_Watch_Company
Datatrak was a hyperbolic radio navigation system similar to Decca, which operated on frequencies between 130 kHz and 150 kHz in the LF-range. Datatrak
Datatrak
Approximate nearest neighbor search algorithm
use local information to move toward a target. Jon Kleinberg's work on navigation in small-world networks is an important example of this research area
Hierarchical navigable small world
Hierarchical_navigable_small_world
Mechanical analog computer
(ln) and exponential (ex) scales. Others feature scales for calculating hyperbolic functions. On linear rules, the scales and their labeling are highly standardized
Slide_rule
Mathematical function that preserves angles
rotations. All these transformations are conformal since hyperbolic rotations preserve hyperbolic angle, (called rapidity) and the other rotations preserve
Conformal_map
Measured time difference as explained by relativity theory
are of practical concern, for instance in the operation of satellite navigation systems such as GPS and Galileo. Time dilation is a relationship between
Time_dilation
Equilibrium points near two orbiting bodies
orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape
Lagrange_point
Transmitter in Girona Province, Spain
in 1962. It closed down in June 1995. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Estartit_Loran-C_transmitter
Framework of distances and directions
type of geometry that does not include the parallel postulate, called hyperbolic geometry. In this geometry, an infinite number of parallel lines pass
Space
off the coast of Schleswig-Holstein. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Rantum_Loran-C_transmitter
Geometry of the surface of a sphere
dimensional spheres. Long studied for its practical applications to astronomy, navigation, and geodesy, spherical geometry and the metrical tools of spherical trigonometry
Spherical_geometry
Equation used in relativistic physics
accounted in terms of the hyperbolic tangent function tanh which takes hyperbolic angle (rapidity) as an argument. In fact, the hyperbolic tangent of rapidity
Velocity-addition_formula
Topics referred to by the same term
pollution Non-Euclidean crystallographic group, a group of symmetries in hyperbolic geometry Numerical Electromagnetics Code, a computer program used to simulate
NEC_(disambiguation)
Curved path of an object around a point
comets, meteoroids, and even space debris. A comet in a parabolic or hyperbolic orbit about a barycenter is not gravitationally bound to the star and
Orbit
Labrador Sea and Icelandic Loran-C chains. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Angissoq_Loran-C_transmitter
Earth-centered orbit above low Earth orbit and below geostationary orbit
non-gravitational perturbing force. Other perturbing forces include: Earth's albedo, navigation antenna thrust, and thermal effects related to heat re-radiation. The
Medium_Earth_orbit
Branch of astronomy
are parabolic and hyperbolic. This is useful for calculating the behaviour of planets and comets and such (parabolic and hyperbolic orbits are conic section
Celestial_mechanics
Set of points equidistant from a center
Spherical geometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is a smooth surface
Sphere
December 2015. It had a power of 400 KW. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Bø_Loran-C_transmitter
Geocentric orbit with an altitude entirely above that of a geosynchronous orbit
astronomy and Earth science, while also enabling global communication and navigation systems. The Moon's Hill sphere is entered at a distance to the Moon of
High_Earth_orbit
Geometry of figures on the surface of a sphere
distance formula. Air navigation Celestial navigation Ellipsoidal trigonometry Great-circle distance or spherical distance Hyperbolic triangle Lenart sphere
Spherical_trigonometry
Former British radar research organization
invasion. He received the Pioneer Award of the IEEE in 1966 for hyperbolic radio navigation. G. W. A. Dummer, electronics engineer. He developed the plan
Telecommunications Research Establishment
Telecommunications_Research_Establishment
Physics problem related to laws of motion and gravity
1978.27.27030. Hulkower, Neal D. (1980). "Central Configurations and Hyperbolic-Elliptic Motion in the Three-Body Problem". Celestial Mechanics. 21 (1):
Three-body_problem
Demolished tower in New York, US
Mast". www.geocaching.com. Retrieved 2024-02-23. http://www.jproc.ca/hyperbolic/loran_c_history.html https://web.archive.org/web/20050317143111/http://www
Forestport_Tower
2024 book
Foreign Policy describes Unit X as “readable and insightful” but “at times hyperbolic”. But the review insists that commercial technology has not yet revolutionized
Unit_X_(book)
and the complex logarithm. Trigonometric functions may be deduced from hyperbolic functions with complex arguments. The formulae for the relations are shown
List of trigonometric identities
List_of_trigonometric_identities
Loran-C radio navigation transmitter in Ejde
North Atlantic and is part of Denmark. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Ejde_Loran-C_transmitter
Orbit around Earth
strictly defined for all circular and elliptical orbits, and parabolic and hyperbolic trajectories. Equatorial plane as used here, an imaginary plane extending
Geocentric_orbit
American attorney, investment banker, and scientist (1887–1975)
philanthropist, scientist, physicist, inventor of the LORAN Long Range Navigation System and a lifelong patron of scientific research. He established the
Alfred_Lee_Loomis
Particular mapping that projects a sphere onto a plane
coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane. Intuitively, the stereographic projection is a way of picturing
Stereographic_projection
Space navigation technique
orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit Equations Dynamical friction Escape
Gravity_assist
2005 non-fiction book by Ray Kurzweil
has been shown that the global acceleration until recently followed a hyperbolic rather than exponential pattern. Theodore Modis says "nothing in nature
The_Singularity_Is_Near
Deepest known point of Earth's seabed
Earth Beneath the Sea, page 417, Figure 2, 1963 "Loran-C Introduction". Hyperbolic Radionavigation Systems. Archived from the original on 10 June 2021. Retrieved
Challenger_Deep
Hypothetical travel between stars or planetary systems
approaches the speed of light (which it cannot exceed). It will undergo hyperbolic motion. The ship will be close to the speed of light after about a year
Interstellar_travel
Orbit keeping the satellite at a fixed longitude above the equator
Today, hundreds of geosynchronous satellites provide remote sensing, navigation and communications. Though most populated land locations on the planet
Geosynchronous_orbit
Transmission facility on the Norwegian island of Jan Mayen
2015. The mast was demolished in 2017. Loran-C is a system of hyperbolic radio navigation which developed from the earlier LORAN system. It uses low frequency
Jan_Mayen_Loran-C_transmitter
Mathematical function, inverse of an exponential function
the tradition of logarithms in prosthaphaeresis, leading to the term "hyperbolic logarithm", a synonym for natural logarithm. Soon the new function was
Logarithm
Hydrodynamics — Hydrostatics — Hyperbolic partial differential equation — Hypersonic — HyShot — Impulse — Inertial navigation system — Instrument landing
Index of aerospace engineering articles
Index_of_aerospace_engineering_articles
English sailor and samurai (1564–1620)
discovery of his alleged tomb in Japan led to a proliferation of myths and hyperbolic stories. Soon the public in England became embarrassed by the lack of
William_Adams_(samurai)
Periodic, three-dimensional orbit
CAPSTONE (Cislunar Autonomous Positioning System Technology Operations and Navigation Experiment), the spacecraft became the first spacecraft to operate in
Near-rectilinear_halo_orbit
Quasi-periodic orbital trajectory
Sources disagree. Astronomy portal "ESA Science & Technology: Orbit/Navigation". European Space Agency. 14 June 2009. Retrieved 2009-06-12. "A230242
Lissajous_orbit
First airborne, ground scanning radar system WWII
bombing. This allowed attacks outside the range of the various radio navigation aids like Gee or Oboe, which were limited to about 350 kilometres (220 mi)
H2S_(radar)
Computation machine that uses continuously varying data technology
transcendental functions such as logarithms and exponentials, circular and hyperbolic trigonometry and other functions. Slide rules have been largely rendered
Analog_computer
Passage of an object through the gases of an atmosphere from outer space
atmospheres, strong gravity, or both factors complicate high-velocity hyperbolic entry, such as the atmospheres of Venus, Titan and the giant planets.
Atmospheric_entry
bookkeeping was pioneered in the Jewish community of the medieval Middle East. Hyperbolic geometry: The theorems of Ibn al-Haytham (Alhacen), Omar Khayyám and Nasīr
List of inventions in the medieval Islamic world
List_of_inventions_in_the_medieval_Islamic_world
French mathematician, physicist and engineer (1854–1912)
conjecture, proven in 2003 by Grigori Perelman. Poincaré recurrence theorem hyperbolic geometry Fuchsian groups number theory the three-body problem the theory
Henri_Poincaré
Open source Android applications
Media is proprietary, but free for personal use. HyperRogue Roguelike in hyperbolic plane ? Yes GPLv2+ ? Luanti Sandbox similar to Minecraft Yes Yes ? OpenArena
List of free and open-source Android applications
List_of_free_and_open-source_Android_applications
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
Girl/Female
American, Australian, Christian, German, Latin
Ever Ruler; Honorable Ruler; The Heather Plant
Boy/Male
Biblical
Sign; or coming of God.
Girl/Female
Indian
Breeze, Nature, Silver, Pure
Boy/Male
English Irish
Surname derived from a medieval given name.
Boy/Male
British, English, French, Jamaican
Son of the Nobleman
Boy/Male
Indian, Telugu
Lord Vishnu; Lucky
Girl/Female
Tamil
Tasteful
Surname or Lastname
Americanized spelling of German Kast.English (Essex, Kent)
Americanized spelling of German Kast.English (Essex, Kent) : possibly a nickname from Norman caste ‘chaste’, ‘virtuous’ (from Old French chaste).Possibly an altered spelling of French Caste, cognate with 2.
Girl/Female
Celtic Russian
Pale.
Girl/Female
Indian
Early morning fragrance or entertaining companion or wind, Enchanting
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
HYPERBOLIC NAVIGATION
n.
A surface of the second order, which is cut by certain planes in hyperbolas; also, the solid, bounded in part by such a surface.
p. pr. & vb. n.
of Hyperbolize
a.
Belonging to the hyperbola; having the nature of the hyperbola.
a.
Having some property that belongs to an hyperboloid or hyperbola.
v. t.
To state or represent hyperbolically.
n.
A figure of speech in which the expression is an evident exaggeration of the meaning intended to be conveyed, or by which things are represented as much greater or less, better or worse, than they really are; a statement exaggerated fancifully, through excitement, or for effect.
a.
Alt. of Hyperbolical
n.
The use of hyperbole.
n.
Diminution; a species of hyperbole, representing a thing as being less than it really is.
v. i.
To speak or write with exaggeration.
a.
Having the form, or nearly the form, of an hyperbola.
imp. & p. p.
of Hyperbolize
n.
A figure by which a grave and magnificent word is put for the proper word; amplification; hyperbole.
n.
One who uses hyperboles.
a.
Exaggerated; excessive; hyperbolical.
a.
Relating to, containing, or of the nature of, hyperbole; exaggerating or diminishing beyond the fact; exceeding the truth; as, an hyperbolical expression.
adv.
In the form of an hyperbola.
n.
The act of exaggerating; the act of doing or representing in an excessive manner; a going beyond the bounds of truth reason, or justice; a hyperbolical representation; hyperbole; overstatement.
a.
Of or pertaining to an hyperbaton; transposed; inverted.
n.
A curve formed by a section of a cone, when the cutting plane makes a greater angle with the base than the side of the cone makes. It is a plane curve such that the difference of the distances from any point of it to two fixed points, called foci, is equal to a given distance. See Focus. If the cutting plane be produced so as to cut the opposite cone, another curve will be formed, which is also an hyperbola. Both curves are regarded as branches of the same hyperbola. See Illust. of Conic section, and Focus.