[permalink] [id link]
If Cartesian coordinates in SI units are used, then the components of the position four-vector are given by: x < sup > 0 </ sup > = t, x < sup > 1 </ sup > = x, x < sup > 2 </ sup > = y, and x < sup > 3 </ sup > = z, where t is time in seconds, and x, y, and z are distances in meters.
from
Wikipedia
Some Related Sentences
If and Cartesian
If ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, x < sub > 3 </ sub >) are the Cartesian coordinates and ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, u < sub > 3 </ sub >) are the orthogonal coordinates, then
If ( x, y ) are the Cartesian coordinates of a point, then (− x, y ) are the coordinates of its reflection across the second coordinate axis ( the Y axis ), as if that line were a mirror.
To make a figure larger or smaller is equivalent to multiplying the Cartesian coordinates of every point by the same positive number m. If ( x, y ) are the coordinates of a point on the original figure, the corresponding point on the scaled figure has coordinates
If the transverse axis of any hyperbola is aligned with the x-axis of a Cartesian coordinate system and is centered on the origin, the equation of the hyperbola can be written as
If a coordinate is not a Cartesian coordinate, the associated generalized momentum component does not necessarily have the dimensions of linear momentum.
If the origin of the Cartesian coordinate system is taken to be at the point of suspension of the first pendulum, then the centre of mass of this pendulum is at:
If both input and output are real numbers, this ordered pair can be viewed as the Cartesian coordinates of a point on the graph of the function.
If are the usual orthogonal Cartesian coordinates, the i th row ( i = 1, ..., m ) of this matrix corresponds to the gradient of the i < sup > th </ sup > component function F < sub > i </ sub >:.
If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress, in the Cartesian coordinate system, is the tensor
If we restrict the local coordinates to be Cartesian coordinates with the same scale centered at the point of interest, the metric tensor is the Kronecker delta.
If a point has the 3D Cartesian coordinates then its transformation for a single direction to a curvilinear reference system of radius R with linear distortion is,
If Nietzsche's response to Cartesian dualism, enlightenment subjectivity ( i. e., Kant ), reductive materialism ( i. e., Marx ), and reductive idealism ( i. e., Hegel ) is not the only nineteenth-century response, it is one of the most effective.
If Cartesian coordinates are used, this equation is modified to incorporate the change in arc length for a spherical gradient, to each physical dimension:
If a standard right-handed Cartesian coordinate system is used, with the x axis to the right and the y axis up, the rotation R ( θ ) is counterclockwise.
If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R ( θ ) is clockwise.
If we take the fixed point as the origin of a Cartesian coordinate system, then every point can be given coordinates as a displacement from the origin.
If we adopt Cartesian coordinates with line element with corresponding wave operator on the flat background, or Minkowski spacetime, so that the line element of the curved spacetime is, then the Ricci scalar of this curved spacetime is just
If you consider an ellipsoid sitting at an angle in a Cartesian grid then you can consider the projection of that ellipse onto the three axes.
If the fluid is incompressible and viscosity is constant across the fluid, the equation governing the shear stress ( in Cartesian coordinates ) is
If and coordinates
If certain coordinate systems are used, for instance, polar-toroidal coordinates ( common in plasma physics ) using the notation ∇ × F will yield an incorrect result.
If the coordinates represent spatial positions ( displacements ), it is common to represent the vector from the origin to the point of interest as.
If y is a point where the vector field v ( y ) ≠ 0, then there is a change of coordinates for a region around y where the vector field becomes a series of parallel vectors of the same magnitude.
If instead we use polar coordinates with the origin at one focus, with the angular coordinate still measured from the major axis, the ellipse's equation is
If the coordinates are chosen badly, the laws of motion may be more complex than necessary.
If the generalized coordinates are represented as a vector and time differentiation is represented by a dot over the variable, then the equations of motion ( known as the Lagrange or Euler – Lagrange equations ) are a set of equations:
If you change units ( a special case of a change of coordinates ) from meters to milimeters, a scale factor of 1 / 1000, a displacement of 1 m becomes 1000 mm – a contravariant change in numerical value.
If a curve is defined in polar coordinates as, then its curvature is
If the manifold M is smooth ( respectively analytic )--- that is, the change of coordinates are smooth ( respectively analytic )--- then one can make sense of the notion of smooth ( respectively analytic ) vector fields.
If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be in nuclear coordinates.
If a multivariate dataset is visualised as a set of coordinates in a high-dimensional data space ( 1 axis per variable ), PCA can supply the user with a lower-dimensional picture, a " shadow " of this object when viewed from its ( in some sense ) most informative viewpoint.
If this window contains windowless embedded objects, the message may have to be relayed to such an object if the coordinates of the mouse-pointer are over this object.
If those coordinates are placed on a map, they are right outside Secor.
If these texture coordinates are linearly interpolated across the screen, the result is affine texture mapping.
If a point of an object has coordinates ( x, y, z ) then the image of this point ( as reflected from the mirror in y, z plane ) has coordinates (- x, y, z ) – so mirror reflection is a reversal of the coordinate axis perpendicular to the mirror's surface.
If the coordinates are changed, the boundary of the region of space – time over which the Lagrangian is being integrated also changes ; the original boundary and its transformed version are denoted as Ω and Ω ’, respectively.
If and SI
If the current has some thickness, the proper formulation of the Biot – Savart law ( again in SI units ) is:
His gravestone features a paraphrase of Christopher Wren's epitaph: " SI QUÆRIS MONUMENTUM, CIRCUMSPICE " (" If you seek his monument, look around you ").
** After Princeton's stunning knockout of the UCLA men's basketball team in the 1996 NCAA tournament, SI wrote " If there really is a hoop heaven, the house band would be Princeton's, troubadours in straw hats who played the theme from " Underdog " late in the Tigers ' victory.
If all quantities are expressed logarithmically in decibels instead of SI units, the above equation becomes
If and units
If the artist would study his work more thoroughly and move certain units in his design, often only slightly, finer pictures would result.
If so they are dispatched to available execution units, resulting in the ability for several instructions to be executed simultaneously.
If the tops of the rock units within the folds remain pointing upwards, they are called anticlines and synclines, respectively.
If some of the units in the fold are facing downward, the structure is called an overturned anticline or syncline, and if all of the rock units are overturned or the correct up-direction is unknown, they are simply called by the most general terms, antiforms and synforms.
If the units b are single bits, then F ( S, b ) could be, for instance
If c, h, and e were all changed so that the values they have in metric ( or any other ) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World.
If a point X is located on a parabola which has focal length and if is the perpendicular distance from X to the axis of symmetry of the parabola, then the lengths of arcs of the parabola which terminate at X can be calculated from and as follows, assuming they are all expressed in the same units.
If the instrument is designed to measure the spectrum in absolute units rather than relative units, then it is typically called a spectrophotometer.
If Imperial units are used, and if torque is in pounds-force feet and rotational speed in revolutions per minute, the above equation gives power in foot pounds-force per minute.
If the diad consists of two identically oriented units, the diad is called a meso diad reflecting similar features as a meso compound.
If the diad consists of units oriented in opposition, the diad is called a racemo diad as in a racemic compound.
If the " amount " of propellant is given in terms of mass ( such as kilograms ), then specific impulse has units of velocity.
If it is given in terms of force ( such as kiloponds ), then specific impulse has units of time.
If a mapping is available, presentation service data units are encapsulated into session protocol data units, and passed down the stack. This layer provides independence from data representation ( e. g., encryption ) by translating between application and network formats.
If the budget does not allow for two identical UPS units then it is common practice to plug one power supply into mains power and the other into the UPS.
If the latter is the case, then as a consumer decreases consumption of one good in successive units, successively larger doses of the other good are required to keep satisfaction unchanged.
If the reaction is first order it has the units s < sup >− 1 </ sup >, and for that reason it is often called the frequency factor or attempt frequency of the reaction.
If the calibration is performed at 100 units, the 1 % standard would actually be anywhere between 99 and 101 units.
The Gaussian integers form a principal ideal domain with units 1, − 1, i, and − i. If x is a Gaussian integer, the four numbers x, ix, − x, and − ix are called the associates of x.
If the source document is subsequently modified, then those text units that have not changed can be directly transferred to the new target version of the document without the need for any translator interaction.
0.469 seconds.