It sounds like you are not actually using time in your plot, but the problem is that longitudes wrap around -180/180. This can be solved using coord_map rather than coord_polar and make sure that longitudes are not wrapped.
Download packages and generate sample data
library("ggplot2") library("dplyr") south_map <- map_data("world") %>% group_by(group) %>% filter(min(lat) <= -20) set.seed(123) track <- data.frame(long = cumsum(c(210, unlist(lapply(c(1, -1), function(x) { rnorm(50, x * 4, 4) })))) %% 360 - 180, lat = cumsum(c(-50, rnorm(100, 0.4, 2))), A1 = sample(1:3, 101, replace = TRUE))
Make sure the coordinates do not wrap around:
track_new <- track long_diff <- diff(track$long) long_diff[long_diff < -180] <- long_diff[long_diff < -180] + 360 long_diff[long_diff > 180] <- long_diff[long_diff > 180] - 360 track_new$long <- cumsum(c(track$long[1], long_diff))
Plot using an aziquidistant projection. Note that this assumes the North Pole in the center, so the latitudes are inverted and then adjusted using the scale.
ggplot(track_new, aes(x = long, y = -lat)) + geom_polygon(aes(group = group), data = south_map, colour = "grey", fill = "gainsboro") + coord_map("azequidistant") + geom_point(aes(colour = factor(A1)), size = 2) + geom_path(colour = "grey", size = 1) + scale_x_continuous(breaks = NULL) + scale_y_continuous("latitude", breaks = 25 * 0:3, labels = -25 * 0:3)
The final plot:

Just for fun, I thought it would be interesting to create an animation of this image. Here is the code for this:
track_new$alpha <- 1 # Setup longitude labels long_labels <- data.frame(long = 45 * -3:4, lat = -22.5) long_labels$label <- long_labels$long long_labels$label[8] <- "\U00B1 180" long_labels$angle <- long_labels$long + 67.5 + 180 * (long_labels$long >= 45) # Set up the basic plot p <- ggplot(track_new, aes(x = long, y = -lat)) + geom_polygon(aes(group = group), data = south_map, colour = "grey", fill = "gainsboro") + coord_map("azequidistant", ylim = c(20, 90)) + geom_point(aes(colour = A1, alpha = alpha), size = 2) + geom_path(aes(alpha = alpha), colour = "grey", size = 1) + scale_x_continuous(breaks = NULL) + scale_y_continuous("latitude", breaks = 22.5 * 0:3, labels = -22.5 * 0:3) + scale_alpha_identity(guide = "none") + geom_text(aes(label = label, angle = angle), data = long_labels, colour = "dark blue", alpha = 0.5, size = 4) # Produce the animation p$data$alpha <- 0 for(i in 1:(nrow(track_new) + 10)) { p$data$alpha <- pmax(p$data$alpha - 0.1, 0) if (i <= nrow(track_new)) { p$data$alpha[i] <- 1 } png(file.path("BirdPlots", sprintf("BirdPlot%03d.png", i)), width = 1024, height = 1024, res = 100) print(p) dev.off() if (!(i %% 5)) cat(i, "\n") } # This needs ImageMagick in the system path. For non-Windows systems, you # might be better using system rather than shell shell(paste("convert", file.path("BirdPlots", "BirdPlot*.png"), file.path("BirdPlots", "BirdPlotAnimation.gif")))
And here is the result:

EDIT Corrected Version of ayush Code
track_df2 <- new_df2 long_diff <- diff(new_df2$Longitude) long_diff[long_diff < -180] <- long_diff[long_diff < -180] + 360 long_diff[long_diff > 180] <- long_diff[long_diff > 180] - 360 track_df2$Longitude <- cumsum(c(new_df2$Longitude[1], long_diff)) track_df2$a3_id <- factor(track_df2$a3_id) ggplot(track_df2, aes(x = Longitude, y = -Latitude)) + coord_map("azequidistant", ylim = c(20, 90)) + geom_point(aes(colour = a3_id, alpha = alpha), size = 2) + geom_path(aes(alpha = alpha), colour = "grey", size = 1) + scale_x_continuous(breaks = NULL) + scale_y_continuous(breaks = 22.5 * 0:3, labels = -22.5 * 0:3) + scale_alpha_identity(guide = "none")