| lorentz-package {lorentz} | R Documentation |
The Lorentz Transform in Relativistic Physics
Description
The Lorentz transform in special relativity; also the gyrogroup structure of three-velocities. Performs active and passive transforms and has the ability to use units in which the speed of light is not unity. Includes some experimental functionality for celerity and rapidity. For general relativity, see the 'schwarzschild' package.
Details
The DESCRIPTION file:
| Package: | lorentz |
| Type: | Package |
| Title: | The Lorentz Transform in Relativistic Physics |
| Version: | 1.1-1 |
| Authors@R: | person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="hankin.robin@gmail.com", comment = c(ORCID = "0000-0001-5982-0415")) |
| Suggests: | knitr,testthat,rmarkdown,covr |
| Imports: | emulator (>= 1.2-20),tensor,magic,magrittr |
| Maintainer: | Robin K. S. Hankin <hankin.robin@gmail.com> |
| Description: | The Lorentz transform in special relativity; also the gyrogroup structure of three-velocities. Performs active and passive transforms and has the ability to use units in which the speed of light is not unity. Includes some experimental functionality for celerity and rapidity. For general relativity, see the 'schwarzschild' package. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| VignetteBuilder: | knitr |
| URL: | https://github.com/RobinHankin/lorentz, https://robinhankin.github.io/lorentz/ |
| BugReports: | https://github.com/RobinHankin/lorentz/issues |
| RoxygenNote: | 7.2.3 |
| Author: | Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>) |
Index of help topics:
Extract.3vel Extract or replace parts of three-velocity
Ops.3vel Arithmetic Ops Group Methods for 3vel objects
as.matrix.3vel Coerce 3-vectors and 4-vectors to a matrix
boost Lorentz transformations
c.3vel Combine vectors of three-velocities and
four-velocities into a single vector
celerity Celerity and rapidity
comm_fail Failure of commutativity and associativity
using visual plots
coordnames Coordinate names for relativity
cosines Direction cosines
fourmom Four momentum
fourvel Four velocities
galileo Classical mechanics; Newtonian approximation;
infinite speed of light
gam Gamma correction
gyr Gyr function
lorentz-package The Lorentz Transform in Relativistic Physics
photon Photons
print.3vel Print methods for three-velocities and
four-velocities
r3vel Random relativistic velocities
reflect Mirrors
seq.3vel seq method for three velocities
sol Speed of light and Minkowski metric
threevel Three velocities
transform The energy-momentum tensor
Author(s)
Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)
Maintainer: Robin K. S. Hankin <hankin.robin@gmail.com>
References
Ungar 2006. “Thomas precession: a kinematic effect...”. European Journal of Physics, 27:L17-L20.
-
https://www.youtube.com/watch?v=9Y9CxiukURw&index=68&list=PL9_n3Tqzq9iWtgD8POJFdnVUCZ_zw6OiB
Examples
u <- as.3vel(c(0.3,0.6,-0.1)) # u is a three-velocity
gam(u) # relativistic gamma term for u
U <- as.4vel(u) # U is a four-velocity
B1 <- boost(u) # B1 is the Lorentz transform matrix for u
B1 %*% c(1,0,0,0) # Lorentz transform of zero 4-velocity (=-u)
B2 <- boost(as.3vel(c(-0.1,0.8,0.3)))
B3 <- boost(as.3vel(c(-0.1,0.1,0.9))) # more boosts
Bi <- B1 %*% B2 # Bi is the boost for successive Lorentz transforms
pureboost(Bi) # Decompose Bi into a pure boost...
orthog(Bi) # and an orthogonal matrix
Bj <- B2 %*% B1 # B1 and B2 do not commute...
(B1 %*% B2) %*% B3
B1 %*% (B2 %*% B3) # ...but composition *is* associative
## Three velocities and the gyrogroup
## Create some random three-velocities:
u <- r3vel(10)
v <- r3vel(10)
w <- r3vel(10)
u+v
v+u # Three-velocity addition is not commutative...
u+(v+w) # ... nor associative
(u+v)+w
[Package lorentz version 1.1-1 Index]