Build the class Planet with the Euler ODE solver
library(rODE)
# This code can also be found in the `examples` folder under this name:
#
# Planet.R
#
setClass("Planet", slots = c(
odeSolver = "Euler",
GM = "numeric"
),
contains = c("ODE")
)
setMethod("initialize", "Planet", function(.Object, ...) {
.Object@GM <- 4 * pi * pi
.Object@state <- vector("numeric", 5)
.Object@odeSolver <- Euler(.Object)
return(.Object)
})
setMethod("doStep", "Planet", function(object, ...) {
# Gets the state variables.
object@odeSolver <- step(object@odeSolver)
object@state <- object@odeSolver@ode@state
object@rate <- object@odeSolver@ode@rate
invisible(object)
})
setMethod("init", "Planet", function(object, initState, ...) {
object@state <- object@odeSolver@ode@state <- initState
# initialize providing the step size
object@odeSolver <- init(object@odeSolver, getStepSize(object@odeSolver))
object@rate <- object@odeSolver@ode@rate
object@state <- object@odeSolver@ode@state
object
})
setMethod("getRate", "Planet", function(object, state, ...) {
# Gets the rate of change using the argument's state variables.
r2 <- state[1] * state[1] + state[3] * state[3]
r3 <- r2 * sqrt(r2)
object@rate[1] <- state[2]
object@rate[2] <- (- object@GM * state[1]) / r3
object@rate[3] <- state[4]
object@rate[4] <- (- object@GM * state[3]) / r3
object@rate[5] <- 1
object@rate
})
setMethod("getState", "Planet", function(object, ...) {
# Gets the state variables.
invisible(object@state)
})
# constructor
Planet <- function() {
new("Planet")
}
## [1] "initialize"
## [1] "doStep"
## [1] "init"
## [1] "getRate"
## [1] "getState"
Run the application PlanetApp
# #################
# This code can also be found in the `examples` folder under this name:
# PlanetApp.R
#
#
PlanetApp <- function(verbose = FALSE) {
# x = 1, AU or Astronomical Units.
# Length of semimajor axis or the orbit of the Earth around the Sun.
x <- 1; vx <- 0; y <- 0; vy <- 6.28; t <- 0
state <- c(x, vx, y, vy, t)
dt <- 0.01
planet <- Planet()
planet@odeSolver <- setStepSize(planet@odeSolver, dt)
planet <- init(planet, initState = state)
# run infinite loop. stop with ESCAPE.
while (planet@state[5] <= 30) { # Earth orbit is 365 days around the sun
for (i in 1:5) { # advances time
planet <- doStep(planet)
}
if (verbose)
cat(sprintf("%12f %12f %12f %12f %12f \n",
planet@state[1], planet@state[2], planet@state[3],
planet@state[4], planet@state[5]))
}
}
PlanetApp()
PlanetApp(verbose = TRUE)
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## 1.066090 2.692640 -3.702819 1.045682 13.200000
## 1.199966 2.653847 -3.647982 1.173204 13.250000
## 1.331801 2.609985 -3.586782 1.300064 13.300000
## 1.461341 2.560976 -3.519254 1.426139 13.350000
## 1.588326 2.506740 -3.445440 1.551294 13.400000
## 1.712494 2.447186 -3.365389 1.675384 13.450000
## 1.833576 2.382223 -3.279157 1.798252 13.500000
## 1.951300 2.311752 -3.186809 1.919727 13.550000
## 2.065388 2.235673 -3.088418 2.039625 13.600000
## 2.175559 2.153879 -2.984067 2.157744 13.650000
## 2.281524 2.066265 -2.873849 2.273865 13.700000
## 2.382991 1.972722 -2.757868 2.387750 13.750000
## 2.479660 1.873142 -2.636242 2.499139 13.800000
## 2.571227 1.767417 -2.509101 2.607751 13.850000
## 2.657384 1.655446 -2.376590 2.713278 13.900000
## 2.737815 1.537129 -2.238870 2.815386 13.950000
## 2.812202 1.412378 -2.096118 2.913714 14.000000
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## 2.941547 1.143271 -1.796328 3.097426 14.100000
## 2.995848 0.998806 -1.639746 3.181927 14.150000
## 3.042793 0.847694 -1.479047 3.260879 14.200000
## 3.082049 0.689941 -1.314520 3.333750 14.250000
## 3.113285 0.525586 -1.146480 3.399973 14.300000
## 3.136173 0.354707 -0.975272 3.458944 14.350000
## 3.150388 0.177433 -0.801270 3.510021 14.400000
## 3.155614 -0.006055 -0.624884 3.552526 14.450000
## 3.151546 -0.195509 -0.446554 3.585750 14.500000
## 3.137890 -0.390610 -0.266761 3.608955 14.550000
## 3.114373 -0.590953 -0.086020 3.621378 14.600000
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## 3.036770 -1.005276 0.276048 3.610773 14.700000
## 2.982265 -1.217945 0.456148 3.586186 14.750000
## 2.917071 -1.433216 0.634746 3.547732 14.800000
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## 2.754220 -1.867591 0.984563 3.426430 14.900000
## 2.656500 -2.084380 1.154267 3.342360 14.950000
## 2.547974 -2.299139 1.319444 3.242026 15.000000
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## 2.299109 -2.716550 1.632923 2.991427 15.100000
## 2.159263 -2.915937 1.779553 2.841028 15.150000
## 2.009611 -3.106810 1.918332 2.674146 15.200000
## 1.850614 -3.287398 2.048444 2.491257 15.250000
## 1.682822 -3.455931 2.169103 2.293087 15.300000
## 1.506872 -3.610693 2.279563 2.080619 15.350000
## 1.323485 -3.750061 2.379133 1.855091 15.400000
## 1.133462 -3.872556 2.467188 1.617987 15.450000
## 0.937673 -3.976887 2.543184 1.371009 15.500000
## 0.737047 -4.061992 2.606663 1.116054 15.550000
## 0.532565 -4.127071 2.657267 0.855164 15.600000
## 0.325238 -4.171614 2.694743 0.590481 15.650000
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## -0.511900 -4.144775 2.712067 -0.462812 15.850000
## -0.718104 -4.089407 2.683862 -0.714543 15.900000
## -0.921184 -4.016480 2.643229 -0.958039 15.950000
## -1.120286 -3.927281 2.590610 -1.191845 16.000000
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## -1.503488 -3.705790 2.451509 -1.625696 16.100000
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## -1.862310 -3.436955 2.271253 -2.009024 16.200000
## -2.031223 -3.288596 2.167317 -2.180493 16.250000
## -2.192565 -3.132903 2.055083 -2.338225 16.300000
## -2.345998 -2.971259 1.935237 -2.482223 16.350000
## -2.491252 -2.804959 1.808464 -2.612631 16.400000
## -2.628116 -2.635200 1.675438 -2.729711 16.450000
## -2.756441 -2.463074 1.536819 -2.833821 16.500000
## -2.876128 -2.289567 1.393248 -2.925391 16.550000
## -2.987127 -2.115563 1.245341 -3.004911 16.600000
## -3.089428 -1.941841 1.093690 -3.072911 16.650000
## -3.183060 -1.769085 0.938861 -3.129946 16.700000
## -3.268083 -1.597888 0.781391 -3.176584 16.750000
## -3.344585 -1.428759 0.621787 -3.213401 16.800000
## -3.412680 -1.262131 0.460530 -3.240966 16.850000
## -3.472499 -1.098368 0.298070 -3.259838 16.900000
## -3.524192 -0.937772 0.134832 -3.270562 16.950000
## -3.567923 -0.780588 -0.028787 -3.273662 17.000000
## -3.603866 -0.627016 -0.192417 -3.269641 17.050000
## -3.632206 -0.477209 -0.355712 -3.258979 17.100000
## -3.653132 -0.331285 -0.518348 -3.242131 17.150000
## -3.666841 -0.189330 -0.680024 -3.219526 17.200000
## -3.673533 -0.051402 -0.840462 -3.191568 17.250000
## -3.673409 0.082466 -0.999401 -3.158638 17.300000
## -3.666674 0.212259 -1.156600 -3.121090 17.350000
## -3.653530 0.337980 -1.311834 -3.079257 17.400000
## -3.634182 0.459646 -1.464896 -3.033448 17.450000
## -3.608831 0.577285 -1.615593 -2.983951 17.500000
## -3.577677 0.690935 -1.763745 -2.931034 17.550000
## -3.540921 0.800642 -1.909187 -2.874946 17.600000
## -3.498757 0.906456 -2.051765 -2.815918 17.650000
## -3.451379 1.008434 -2.191337 -2.754163 17.700000
## -3.398979 1.106634 -2.327769 -2.689880 17.750000
## -3.341743 1.201119 -2.460939 -2.623251 17.800000
## -3.279855 1.291951 -2.590734 -2.554448 17.850000
## -3.213499 1.379194 -2.717048 -2.483626 17.900000
## -3.142851 1.462912 -2.839783 -2.410931 17.950000
## -3.068086 1.543168 -2.958847 -2.336498 18.000000
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## -2.906893 1.693540 -3.185635 -2.182902 18.100000
## -2.820798 1.763778 -3.293206 -2.103961 18.150000
## -2.731256 1.830794 -3.396805 -2.023725 18.200000
## -2.638427 1.894643 -3.496367 -1.942285 18.250000
## -2.542467 1.955379 -3.591834 -1.859725 18.300000
## -2.443533 2.013052 -3.683152 -1.776124 18.350000
## -2.341775 2.067711 -3.770271 -1.691553 18.400000
## -2.237344 2.119401 -3.853142 -1.606081 18.450000
## -2.130387 2.168165 -3.931723 -1.519769 18.500000
## -2.021050 2.214043 -4.005973 -1.432677 18.550000
## -1.909476 2.257073 -4.075853 -1.344857 18.600000
## -1.795806 2.297289 -4.141329 -1.256361 18.650000
## -1.680182 2.334722 -4.202367 -1.167237 18.700000
## -1.562742 2.369401 -4.258937 -1.077528 18.750000
## -1.443622 2.401353 -4.311010 -0.987276 18.800000
## -1.322958 2.430600 -4.358561 -0.896521 18.850000
## -1.200886 2.457163 -4.401564 -0.805301 18.900000
## -1.077540 2.481058 -4.439998 -0.713651 18.950000
## -0.953051 2.502300 -4.473841 -0.621605 19.000000
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## -0.701179 2.536869 -4.527681 -0.436454 19.100000
## -0.574058 2.550210 -4.547644 -0.343413 19.150000
## -0.446323 2.560926 -4.562949 -0.250100 19.200000
## -0.318104 2.569018 -4.573584 -0.156546 19.250000
## -0.189533 2.574482 -4.579537 -0.062781 19.300000
## -0.060742 2.577313 -4.580798 0.031167 19.350000
## 0.068138 2.577502 -4.577358 0.125268 19.400000
## 0.196974 2.575036 -4.569210 0.219492 19.450000
## 0.325634 2.569901 -4.556350 0.313808 19.500000
## 0.453984 2.562080 -4.538772 0.408185 19.550000
## 0.581888 2.551551 -4.516475 0.502590 19.600000
## 0.709211 2.538292 -4.489457 0.596989 19.650000
## 0.835816 2.522275 -4.457720 0.691348 19.700000
## 0.961565 2.503470 -4.421267 0.785629 19.750000
## 1.086318 2.481846 -4.380102 0.879793 19.800000
## 1.209932 2.457366 -4.334231 0.973798 19.850000
## 1.332264 2.429991 -4.283664 1.067599 19.900000
## 1.453170 2.399681 -4.228412 1.161151 19.950000
## 1.572500 2.366390 -4.168488 1.254401 20.000000
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## 1.805833 2.290672 -4.034693 1.439778 20.100000
## 1.919529 2.248140 -3.960862 1.531783 20.150000
## 2.031034 2.202420 -3.882441 1.623245 20.200000
## 2.140189 2.153452 -3.799459 1.714089 20.250000
## 2.246829 2.101174 -3.711949 1.804238 20.300000
## 2.350789 2.045522 -3.619946 1.893606 20.350000
## 2.451897 1.986430 -3.523492 1.982101 20.400000
## 2.549980 1.923828 -3.422633 2.069624 20.450000
## 2.644863 1.857647 -3.317418 2.156066 20.500000
## 2.736363 1.787815 -3.207905 2.241311 20.550000
## 2.824298 1.714258 -3.094155 2.325233 20.600000
## 2.908479 1.636902 -2.976238 2.407696 20.650000
## 2.988715 1.555675 -2.854230 2.488551 20.700000
## 3.064811 1.470502 -2.728213 2.567640 20.750000
## 3.136569 1.381311 -2.598280 2.644791 20.800000
## 3.203785 1.288032 -2.464531 2.719817 20.850000
## 3.266255 1.190599 -2.327076 2.792518 20.900000
## 3.323769 1.088948 -2.186036 2.862680 20.950000
## 3.376115 0.983023 -2.041543 2.930069 21.000000
## 3.423079 0.872774 -1.893740 2.994436 21.050000
## 3.464442 0.758159 -1.742783 3.055515 21.100000
## 3.499988 0.639149 -1.588842 3.113019 21.150000
## 3.529495 0.515726 -1.432102 3.166643 21.200000
## 3.552742 0.387890 -1.272764 3.216061 21.250000
## 3.569509 0.255656 -1.111045 3.260927 21.300000
## 3.579577 0.119065 -0.947179 3.300875 21.350000
## 3.582730 -0.021822 -0.781421 3.335517 21.400000
## 3.578754 -0.166911 -0.614042 3.364448 21.450000
## 3.567441 -0.316077 -0.445339 3.387242 21.500000
## 3.548591 -0.469160 -0.275625 3.403456 21.550000
## 3.522011 -0.625954 -0.105240 3.412632 21.600000
## 3.487522 -0.786210 0.065456 3.414302 21.650000
## 3.444955 -0.949627 0.236078 3.407987 21.700000
## 3.394159 -1.115849 0.406217 3.393205 21.750000
## 3.335003 -1.284457 0.575439 3.369476 21.800000
## 3.267377 -1.454971 0.743288 3.336332 21.850000
## 3.191195 -1.626839 0.909285 3.293317 21.900000
## 3.106403 -1.799439 1.072927 3.240007 21.950000
## 3.012977 -1.972079 1.233691 3.176010 22.000000
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## 2.800315 -2.314335 1.544404 3.014657 22.100000
## 2.681229 -2.482208 1.693226 2.916815 22.150000
## 2.553815 -2.646641 1.836924 2.807341 22.200000
## 2.418263 -2.806614 1.974915 2.686218 22.250000
## 2.274819 -2.961068 2.106618 2.553541 22.300000
## 2.123780 -3.108915 2.231460 2.409528 22.350000
## 1.965499 -3.249059 2.348880 2.254532 22.400000
## 1.800381 -3.380414 2.458337 2.089043 22.450000
## 1.628889 -3.501925 2.559320 1.913693 22.500000
## 1.451534 -3.612593 2.651351 1.729254 22.550000
## 1.268878 -3.711495 2.733992 1.536634 22.600000
## 1.081525 -3.797807 2.806855 1.336862 22.650000
## 0.890120 -3.870828 2.869604 1.131080 22.700000
## 0.695338 -3.929992 2.921963 0.920519 22.750000
## 0.497883 -3.974887 2.963719 0.706479 22.800000
## 0.298473 -4.005263 2.994726 0.490303 22.850000
## 0.097836 -4.021037 3.014902 0.273352 22.900000
## -0.103299 -4.022294 3.024237 0.056978 22.950000
## -0.304209 -4.009280 3.022786 -0.157506 23.000000
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## -0.702557 -3.942166 2.988068 -0.575856 23.100000
## -0.898657 -3.889258 2.955219 -0.777470 23.150000
## -1.091869 -3.824424 2.912413 -0.972722 23.200000
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## -1.467356 -3.662391 2.798312 -1.340892 23.300000
## -1.648604 -3.567022 2.727800 -1.512507 23.350000
## -1.824913 -3.463350 2.648885 -1.675151 23.400000
## -1.995887 -3.352331 2.562023 -1.828482 23.450000
## -2.161179 -3.234906 2.467685 -1.972273 23.500000
## -2.320486 -3.111990 2.366350 -2.106400 23.550000
## -2.473552 -2.984461 2.258502 -2.230832 23.600000
## -2.620162 -2.853148 2.144627 -2.345622 23.650000
## -2.760144 -2.718833 2.025202 -2.450894 23.700000
## -2.893361 -2.582239 1.900702 -2.546829 23.750000
## -3.019714 -2.444032 1.771588 -2.633663 23.800000
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## -3.251583 -2.165153 1.501303 -2.781151 23.900000
## -3.357047 -2.025524 1.360988 -2.842436 23.950000
## -3.455537 -1.886375 1.217767 -2.895868 24.000000
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## -3.631744 -1.611017 0.924132 -2.980589 24.100000
## -3.709577 -1.475446 0.774436 -3.012594 24.150000
## -3.780665 -1.341636 0.623270 -3.038168 24.200000
## -3.845102 -1.209804 0.470948 -3.057659 24.250000
## -3.902990 -1.080135 0.317768 -3.071405 24.300000
## -3.954440 -0.952782 0.164010 -3.079736 24.350000
## -3.999571 -0.827874 0.009939 -3.082968 24.400000
## -4.038507 -0.705511 -0.144197 -3.081404 24.450000
## -4.071377 -0.585776 -0.298163 -3.075333 24.500000
## -4.098314 -0.468729 -0.451740 -3.065033 24.550000
## -4.119454 -0.354416 -0.604722 -3.050765 24.600000
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## -4.144889 -0.134102 -0.908138 -3.011307 24.700000
## -4.149464 -0.028125 -1.058221 -2.986572 24.750000
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## -4.143022 0.175478 -1.354343 -2.928133 24.850000
## -4.132284 0.273131 -1.500094 -2.894809 24.900000
## -4.116719 0.368048 -1.644127 -2.858982 24.950000
## -4.096461 0.460256 -1.786322 -2.820814 25.000000
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## -4.042410 0.636673 -2.064747 -2.738048 25.100000
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## -3.883825 0.958550 -2.594981 -2.550449 25.300000
## -3.834402 1.032805 -2.721493 -2.499614 25.350000
## -3.781316 1.104657 -2.845434 -2.447403 25.400000
## -3.724684 1.174148 -2.966740 -2.393904 25.450000
## -3.664623 1.241320 -3.085345 -2.339196 25.500000
## -3.601251 1.306215 -3.201193 -2.283358 25.550000
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## -3.316862 1.543810 -3.635947 -2.050031 25.750000
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## -3.074131 1.699980 -3.930666 -1.866177 25.900000
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## -2.524790 1.959601 -4.435181 -1.480990 26.200000
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## -2.223303 2.064570 -4.643415 -1.281511 26.350000
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## -1.907179 2.153802 -4.821465 -1.078402 26.500000
## -1.798955 2.180134 -4.874019 -1.009992 26.550000
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## -1.010117 2.318061 -5.145113 -0.523043 26.900000
## -0.893944 2.331247 -5.169855 -0.452505 26.950000
## -0.777144 2.342821 -5.191066 -0.381765 27.000000
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## -0.541984 2.361140 -5.222857 -0.239727 27.100000
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## -0.305283 2.373020 -5.240413 -0.097026 27.200000
## -0.186555 2.376539 -5.243834 -0.025457 27.250000
## -0.067683 2.378440 -5.243673 0.046241 27.300000
## 0.051251 2.378715 -5.239925 0.118057 27.350000
## 0.170166 2.377358 -5.232584 0.189979 27.400000
## 0.288980 2.374359 -5.221645 0.261994 27.450000
## 0.407612 2.369708 -5.207104 0.334088 27.500000
## 0.525978 2.363394 -5.188957 0.406250 27.550000
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## 0.878643 2.334330 -5.112850 0.622995 27.700000
## 0.995104 2.321215 -5.080255 0.695279 27.750000
## 1.110874 2.306356 -5.044046 0.767555 27.800000
## 1.225867 2.289732 -5.004223 0.839805 27.850000
## 1.339992 2.271320 -4.960788 0.912010 27.900000
## 1.453161 2.251098 -4.913744 0.984150 27.950000
## 1.565282 2.229039 -4.863095 1.056204 28.000000
## 1.676263 2.205117 -4.808846 1.128149 28.050000
## 1.786010 2.179303 -4.751002 1.199961 28.100000
## 1.894429 2.151568 -4.689570 1.271615 28.150000
## 2.001421 2.121879 -4.624559 1.343082 28.200000
## 2.106890 2.090203 -4.555979 1.414333 28.250000
## 2.210734 2.056505 -4.483841 1.485336 28.300000
## 2.312852 2.020749 -4.408159 1.556057 28.350000
## 2.413141 1.982896 -4.328946 1.626458 28.400000
## 2.511495 1.942907 -4.246221 1.696500 28.450000
## 2.607806 1.900740 -4.160002 1.766140 28.500000
## 2.701964 1.856353 -4.070309 1.835332 28.550000
## 2.793858 1.809701 -3.977166 1.904027 28.600000
## 2.883373 1.760739 -3.880600 1.972171 28.650000
## 2.970393 1.709420 -3.780638 2.039708 28.700000
## 3.054799 1.655695 -3.677312 2.106575 28.750000
## 3.136470 1.599515 -3.570658 2.172705 28.800000
## 3.215282 1.540831 -3.460713 2.238029 28.850000
## 3.291109 1.479591 -3.347519 2.302468 28.900000
## 3.363823 1.415743 -3.231122 2.365940 28.950000
## 3.433290 1.349236 -3.111572 2.428357 29.000000
## 3.499379 1.280017 -2.988924 2.489623 29.050000
## 3.561951 1.208035 -2.863238 2.549635 29.100000
## 3.620868 1.133239 -2.734577 2.608284 29.150000
## 3.675989 1.055578 -2.603014 2.665453 29.200000
## 3.727168 0.975004 -2.468623 2.721014 29.250000
## 3.774259 0.891471 -2.331489 2.774832 29.300000
## 3.817114 0.804934 -2.191701 2.826764 29.350000
## 3.855582 0.715354 -2.049356 2.876654 29.400000
## 3.889508 0.622695 -1.904561 2.924338 29.450000
## 3.918740 0.526926 -1.757428 2.969640 29.500000
## 3.943121 0.428023 -1.608080 3.012372 29.550000
## 3.962494 0.325969 -1.456651 3.052337 29.600000
## 3.976701 0.220756 -1.303282 3.089324 29.650000
## 3.985584 0.112386 -1.148127 3.123109 29.700000
## 3.988985 0.000874 -0.991350 3.153458 29.750000
## 3.986749 -0.113754 -0.833129 3.180123 29.800000
## 3.978719 -0.231453 -0.673652 3.202844 29.850000
## 3.964744 -0.352163 -0.513122 3.221349 29.900000
## 3.944675 -0.475805 -0.351756 3.235355 29.950000
## 3.918366 -0.602274 -0.189784 3.244568 30.000000