where and are the radial and angular elliptic coordinates

See radial elliptic trajectory, free-fall time.

As an orbit, this is a radial elliptic trajectory.

This includes the radial elliptic orbit, with eccentricity equal to 1.

Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance ( such as gravity ), has an orbit that is a conic section ( i. e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory ) with the central body located at one of the two foci, or the focus ( Kepler's first law ).

For any Kepler orbit ( elliptic, parabolic, hyperbolic or radial ), the vis viva equation is as follows:

See radial hyperbolic trajectory

See radial parabolic trajectory.

A classical trajectory in the radial plane for

This velocity () is closely related to the orbital velocity of a body in a circular orbit of the radius equal to the radial position of orbiting body on the parabolic trajectory:

A radial parabolic trajectory is a non-periodic trajectory on a straight line where the relative velocity of the two objects is always the escape velocity.

A radial hyperbolic trajectory is a non-periodic trajectory on a straight line where the relative speed of the two objects always exceeds the escape velocity.

A purely radial trajectory is an example of a degenerate ellipse with an eccentricity of 1 and semi-major axis.

For a discussion of the Kepler problem specific to radial orbits, see: Radial trajectory.

For example, arrow 17 in Figure 3 portrays the proximal radial epiphysis for boy 34, whereas the same epiphysis for girl 2 is portrayed by arrow 18 in Figure 4.

The inflorescence is crowded with quite large, radial symmetrical flowers, which face upwards.

# The Slater-type orbital ( STO ) is a form without radial nodes but decays from the nucleus as does the hydrogen-like orbital.

where m and n are nonnegative integers with, is the azimuthal angle in radians, and is the normalized radial distance.

For the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

Because of the cross product, L is a pseudovector perpendicular to both the radial vector r and the momentum vector p and it is assigned a sign by the right-hand rule.

Angular momenta of a classical object .< p > Left: intrinsic " spin " angular momentum S is really orbital angular momentum of the object at every point ,</ p >< p > right: extrinsic orbital angular momentum L about an axis ,</ p >< p > top: the moment of inertia tensor | moment of inertia tensor I and angular velocity ω ( L is not always parallel to ω )</ p >< p > bottom: momentum p and it's radial position r from the axis .</ p > The total angular momentum ( spin + orbital ) is J.

* Some curves that seem simple, such as the circle, cannot be described exactly by a Bézier or piecewise Bézier curve ; though a four-piece cubic Bézier curve can approximate a circle ( see Bézier spline ), with a maximum radial error of less than one part in a thousand, when each inner control point ( or offline point ) is the distance horizontally or vertically from an outer control point on a unit circle.

The height of the water h = h ( r ) is a function of the radial distance r from the axis of rotation Ω, and the aim is to determine this function.

That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation.

In the case of a central force, relative to the origin of the polar coordinate system, can be replaced by, meaning the entire force is the component in the radial direction.

In such a frame, the observed is zero and alone is treated as the acceleration: so in the equation of motion, the term is " reincarnated on the force side of the equation ( with opposite signs, of course ) as the centrifugal force mω < sup > 2 </ sup > r in the radial equation ": The " reincarnation " on the force side of the equation is necessary because, without this force term, observers in the rotating frame would find they could not predict the motion correctly.

When the angular velocity of this co-rotating frame is not constant, that is, for non-circular orbits, other fictitious forces — the Coriolis force and the Euler force — will arise, but can be ignored since they will cancel each other, yielding a net zero acceleration transverse to the moving radial vector, as required by the starting assumption that the vector co-rotates with the planet.

In the special case of circular orbits, in order for the radial distance to remain constant the outward centrifugal force must cancel the inward force of gravity ; for other orbit shapes, these forces will not cancel, so r will not be constant.

As the front truck cylinders were now using boiler pressure steam, special arrangements were necessary to deliver it, through the truck pivot pin where only radial movement took place.

The " Gran Sport " package was still available as a separate option package consisting of a ride-and-handling package that included a rear stabilizer bar, JR78-15 whitewall steel-belted radial tires, a specially tuned " radial roadability " suspension, additional sound insulation and special " Gran Sport " badging.

Upon completing his thesis, Mayor decided to develop a special spectrograph, CORAVEL, to measure stellar radial velocity.

New options included power brakes, tilt steering wheel, BR78-13B steel belted radial tires, and special custom cloth interior for the Hatchback and Kammback.

The Spyder Equipment package included 2-barrel, Dura-Built 2. 3 litre engine, floor console unit, large front / rear stabilizer bars, special shock absorbers, steel-belted radial ply blackwall tires, wheel opening mouldings ( chrome ), Day-Night inside mirror, Sport Steering Wheel ( 2-spoke wheel ), Special instrumentation and ' stitched ' instrument panel pad with added wood-grain vinyl accents ( standard on 2 + 2 ), Distinctive " Spyder " identification ( script fender emblems, steering wheel horn button insert and Spyder front facia and rear-lock cover )

The 1981 to 1985 Citation X-11 models had legitimate performance upgrades such as a 2-bbl 2. 8 V6 LH7 High Output engine, including Tuned High-Flo Exhaust with Dual-Tipped Muffler, F41 sport suspension, rear spoiler, special axle ratios, special full instrumentation with a 7000 rpm tach, front and back stabilizer bars, 14 " specific alloy wheels with the word " Citation " cast in, Goodyear Eagle GT P215 / 60 R14 radial tires, functional fiberglass cowl induction hood with " High Output V6 " logo and also on the air filter housing on the 81-84 X-11 models, dual sport mirrors, " strobe " style X-11 graphics on the lower side doors and rear spoiler, standard 4-speed overdrive manual or the optional 3-speed automatic, both with special gearing.

This type of symmetry is especially suitable for sessile animals such as the sea anemone, floating animals such as jellyfish, and slow moving organisms such as sea stars ( see special forms of radial symmetry ).

All these animals show bilateral symmetry in their larval stage, but pentalateral symmetry ( a special type of radial symmetry ) as adults.

A special mode is required because the Doppler velocity feedback information must be unlinked from radial movement so that the system can transition from scan to track with no lock.

The GT package was available on the Spirit liftback and included among other features, blacked out exterior trim, radial tires with styled wheels, black leather-wrapped sport steering wheel and console, tachometer and " Rallye " gauges, as well as a special " deep-tone " exhaust system.

It featured special color-matched fender flares and front air dam, ' Rally-Tuned ' suspension with front and rear sway bars, high-effort power steering gears, adjustable Gabriel ( brand name ) ' Strider ' shock absorbers, heavy-duty semi-metallic front disk brakes with ribbed 10x1. 2-inch ( 254x30. 5 mm ) rear drum brakes, unique AMX grille, " Turbocast II " 14x7-inch aluminum road wheels with ER60x14 Goodyear " Flexten " GT radial RWL ( raised white letter ) tires, rear spoiler, special striping package, hood and door decals, console shifted automatic or manual transmission with ' Rallye Gauge ' package ( total of eight dials including an intake-manifold vacuum gauge ), as well as simulated aluminum dash overlays with AMX badge on the glove compartment door.

The AMX included performance DR78 x 14 BSW steel-belted radial tires, front sway bar, vinyl bucket seats, a center floor console, " rally gauges " with tachometer, brushed aluminum instrument panel overlays, black " soft-feel " sports steering wheel, and special trim on the door panels with map pockets.

The special items were: individual reclining seats in velveteen crush fabric with woven accent stripes, custom door trim panels, unique headliner, headlight bezels painted accent color, black trunk carpet, rear sway bar, GR78x15 radial whitewall tires, color-keyed slot styled wheels, body color front and rear bumpers, two-tone paint, landau padded vinyl roof, opera quarter windows with accents, dual remote control mirrors painted body color, Barcelona medallion on glove box door and fenders, carpeting and bumper nerfing strips.

It is also possible to use the ' power of the gods ': when the magic tank is full, the player can use a simple or radial magic attack, and each weapon has a special magic power.