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Parallel Glossary of Space and Time for Classical Physics

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This is the latest draft of a glossary for 3D time compared with 3D space. Modifications include the concept of "base" as a spatial analogue of scalar time.
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  Parallel Glossary of Space and Time for Classical Physics  RA Gillmann, 2019-10-12 General Terms kinematics  is the set of ordered pairs of relative length and duration position, called location  and chronation . event  is a physical occurrence with location and chronation. event order  is a baseline or timeline. body  is a physical entity with location and chronation. motion of a body  is a continuous change of its location and chronation. metric of motion  is the extent of motion as measured by length or duration.  Length Terms    Duration Terms   length  is the extent of a motion as measured by a rigid rod or a measuring wheel. point  is an event with minimum length. angle  ( θ   or ϕ ) is a proportion of a circle between two rays intersecting in a point. angle direction  is the angle from a reference ray.  duration  is the extent of a motion as measured by a stopwatch or clock. instant  is an event with minimum duration. turn angle  (  χ   or ψ  ) is a proportion of a uniform revolution between two rays intersecting in an instant. turn direction  is the turn angle from a reference ray.  base  is an independent length variable of uniform motion; equals the location vector magnitudes of simulbasal  points; symbol s ; adj . basal. basepoint   n . is a base value. baseline  is an ordering of events by their basepoints. spaces  (of length) are baseline intervals.  time  is an independent duration variable of uniform motion; equals the chronation vector magnitudes of simultaneous  instants; symbol t  ; adj . temporal. timepoint   n . is a time value. timeline  is an ordering of events by their timepoints. period  (of duration) is a timeline interval.  space interval  (distance) is (1) the length of uniform motion between two points in 3D space; (2) the absolute difference between two base values; or (3) the magnitude of a displacement vector; symbol s . displacement  is a vector of distance and angle direction between two points.  time interval  (distime) is (1) the duration of uniform motion between two instants in 3D time; (2) the absolute difference between two time values; or (3) the magnitude of a dischronment vector; symbol t  . dischronment  is a vector of distime and turn direction between two instants.  length manifold  (3D space) is a Euclidean manifold of three length dimensions. length-timeline  is a 3D length manifold with a timeline (3+1). length srcin  is a reference point. location  (or length position) of a point in a length manifold is the displacement   vector to it from the srcin point; symbol s .  duration manifold  (3D time) is a Euclidean manifold of three duration dimensions. duration-baseline  is a 3D duration manifold with a baseline (1+3). duration srcin  is a reference instant. chronation  (duration position) of an instant in a duration manifold is the dischronment   vector to it from the srcin instant; symbol t .  simulbaseity is the relation between events with the same basepoint; adjective simulbasal . symbasal , has the same basepoints; verb symbasalize , to make symbasal.  simultaneity  is the relation between events with the same timepoint; adjective simultaneous . synchronous , has the same timepoints; verb synchronize , to make synchronous.  metre  is the SI unit of length, distance, base, or space interval. metreloge  device displays the present basepoint.  second  is the SI unit of duration, distime, or time, or time interval. clock  device displays the present timepoint.  speed  of a motion is the time rate of length change, that is, the ratio of its length to the time unit without regard to direction; symbol v ; units of m/s, km/hr, etc.; timepoint (instantaneous) speed is d s  /d t  , which equals the magnitude of timepoint velocity. pace  of a motion is the space rate of duration change, that is, the ratio of its duration to the base unit without regard to direction; symbol u ; from racing; units of s/m, min/km, etc.; basepoint   pace is d t   /d s , which equals the magnitude of basepoint    legerity . velocity   (vel∙o′∙ci∙ty) of a body in motion is the ratio of its displacement   to the change in time; symbol v ; mean velocity is Δ r /Δ t  ; timepoint (instantaneous) velocity is d s  /d t   = d s  /|d t |; from Latin velocitas , swiftness, rapidity. legerity  ( le·jer′·i·ty ) of a body in motion is the ratio of its dischronment   to the change in baseline; symbol u ; mean legerity is Δ t /Δ s ; basepoint    legerity  is d t  /d s  = d t  /|d s |; from Mid. French legereté  , quickness or lightness in movement. acceleration  is the change in the displacement   per unit of its dischronment magnitude; verb is accelerate  with negative decelerate ; no acceleration is unaccelerated  ; units of m/s²; symbol a ; timepoint acceleration is d v  /d t   = d v  /|d t |.  expedience is the change in the dischronment   per unit of its displacement magnitude; verb is expedite  with negative de-expedite ; no expedience is inexpedienced  ; units of s/m²; symbol b ; basepoint expedience is d u  /d s  = d u  /|d s |.    Parallel Glossary of Space and Time for Classical Physics   circular motion:  base circumference S = wavelength  λ  = v  /   f  ; circular arc s ; base radius R; length angle θ    = s  /R; frequency  f = 1/T = v  /   λ ; angular velocity v = S/T =  λf   ; if S = 1, then v =  f  ; if R = 1, then v = ω   = 2π  f = θ   /  t  .  cyclic motion:  time period T = wave duration  μ  = u  /  h ; rotation time t  ; time radius Q; duration angle ϕ   = t   /Q; periodicity h = 1/S = u  /   μ ; angular legerity u = T/S =  μh ; if T = 1, then u = h ; if Q = 1, then u = ψ   = 2π h  = θ   /  s .  travel distance  (arc length) is the length along a curve. length scale  is a ratio of map distance vs. actual distance. isodistance  line shows equidistant   events. locus  is the set of all points meeting some criteria. travel time  (arc duration) is the duration along a curve. time scale  is a ratio of map time interval vs. actual time interval. isochron  line shows equidistimed   events. chronus  is the set of all instants meeting some criteria.  space mean speed  (SMS) is the harmonic mean of speeds with a common space unit. time mean speed  (TMS) is the arithmetic mean of speeds with a common time unit. time mean pace  (TMP) is the harmonic mean of paces with a common time unit. space mean pace  (SMP) is the arithmetic mean of paces with a common space unit.  reference frame is a method of describing the location, velocity, and acceleration of a body.  reference timeframe  is a method of describing the chronation, legerity, and expedience of a body.  inertia  (linear) is the resistance of a body to any change in its state of motion. inertial system  has bodies at rest or moving with constant velocity.  facilia (linear) is the nonresistance of a body to a change in its state of movement; Latin for easy . facilial   system  has bodies at rest or moving with constant legerity. mass  is the resistance of a body to a change in its condition of motion as a net force is applied; inverse of vass ; units of kg; symbol m .  vass (or spread) is the nonresistance of a body to a change in its condition of movement as a net rush is applied; inverse of mass; from vast; units of kg  ‒  1 ; symbol n . matter  (particle) is a body with mass  that occupies a place; a measure of the energy content of a body.  carrier  (wave) is a body with vass  that fills an occasion; a measure of the reserve content of a body.  moment  is the product of a physical quantity such as mass or force and its space interval from or to a point or axis.  fulment  is the product of a physical quantity such as vass  or rush  and its time interval from or to an instant.  center of mass  (or bathycenter  ) is the normalized moment of mass; R  = (1/   M  ) Σ i   r i  m i . moment of inertia  is the second moment of mass;  I    ≡   Σ i   r  i2   m i .  center of vass  (or elaphrocenter  ) is the normalized fulment of vass; T  = (1/   N  ) Σ i   t i  n i . fulment of facilia  is the second fulment of vass;  J    ≡   Σ i   t  i2   n i .  gravitation  is the mutual force that all bodies have, which is directed toward the mutual center of mass. weight  is the force exerted on a body by gravity.  levitation  is the mutual rush  that all bodies have, which is directed toward the mutual center of vass . elaphra  is the rush  exerted on a body by levity .  momentum  (linear) is the mass  times the velocity ; the time rate of change of the mass-distance moment; Latin; units in kg m s  ‒1 ; symbol p  = m v .  fulmentum   (ful∙men′∙tum) is the   vass  times the legerity ; the length rate of change of the vass-distime fulment; Latin, prop, support; units of kg  ‒1  s m  ‒1 ; symbol q  = n u .  force  is the duration rate of change of momentum ; units in newtons, N = kg m s  ‒2 ; symbol F   ≡  d p  /d t  , e.g., m a .  rush  is the length rate of change of  fulmentum ; units in oldtons , O = kg  ‒1  s m  ‒2 ; symbol R   ≡  d q  /d s , e,g., n b . impulse  is a force F  applied over a duration d t  , or the change in momentum; units N·s; symbol J   ≡   F ·d t   = d p . work  is a force F  applied over a displacement s : W    ≡   F · s ; for a constant force: W = F   d s  = P  d t  ; units: J = N·m.  hustle  is a rush   G  applied over a length d s , or change in  fulmentum ; units O·m; symbol K ≡  R ·d s  = d q . surge  (inverse of work) is a rush   R  applied over a dischronment    t :  X    ≡   R · t ; for a constant rush : Y = R  d t   =  Z   d s ; units O·s.  power  is the ratio of work per unit of time: P   ≡  d W   /d t   = F  · v ; units: Watt, W = J/s = N·m/s.  alacrity  is the ratio of surge per unit of baseline:  Z    ≡  d V   /d s  = R · u ; units: 1/J·m = O·s/m.  energy  is the capacity for doing work; units, J ≡  N·m = W·s; symbol  E  . kinetic energy  KE = ½ m v ².  reserve  (lethargy) is the capacity for surge; units, 1/J ≡  O·s; symbol Q  = 1/   E  . kinetic reserve  KR = ½ n u ².  angular momentum  for a point particle is the moment of momentum, L   ≡   r  × p , the cross product of the particle's location vector, r , and its momentum vector, p  = m v .  angular fulmentum  for a transicle  is the fulment of fulmentum, Γ   ≡   t  × q , the cross product of the particle's chronation  vector, t , and its  fulmentum  vector, q  = n u .  torque  is the moment of force; the rate of change of angular momentum of a body, τ  = I α ; units: N·m.  strophence is the fulment of rush; the rate of change of angular  fulmentum  of a body, σ  = I β ; from Greek strophe , turn + (e) nce.  
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