# Load required libraries
library(ggplot2)
library(animation)

# Define the masses
masses <- data.frame(
  mass = c(5, 2, 10),
  x = c(5, 2, 0),
  y = c(0, 0, 0)
)

# Create a function to rotate the masses
rotate_masses <- function(angle) {
  rotation_matrix <- matrix(c(cos(angle), -sin(angle), sin(angle), cos(angle)), nrow = 2, byrow = TRUE)
  new_positions <- as.data.frame(as.matrix(masses[, c("x", "y")]) %*% rotation_matrix)
  colnames(new_positions) <- c("x", "y")
  return(cbind(masses$mass, new_positions))
}

# Create initial plot
initial_plot <- ggplot() +
  geom_point(data = masses, aes(x = x, y = y, size = mass,col=as.factor(mass)))  +
  theme_void()+
  theme(legend.position = "none")+
  scale_size_continuous(range = c(3, 6)) +

  xlim(-5, 5) +
  ylim(-5, 5) +
  labs(title = "Movement of Masses")

# Create animation frames
frames <- lapply(seq(0, 2 * pi, by = pi / 36), function(angle) {
  rotated_masses <- rotate_masses(angle)
  colnames(rotated_masses) <- c("mass", "x", "y")
  frame <- initial_plot +
    geom_point(data = rotated_masses, aes(x = x, y = y, size = mass, col=as.factor(mass))) +
    theme_void()+
    theme(legend.position = "none")
  return(frame)
})

# Save animation
ani.options(interval = 0.1)
saveGIF({
  for (i in 1:length(frames)) {
    print(frames[[i]])
  }
}, movie.name = "mass_movement0.gif", ani.width = 600, ani.height = 600, ani.units = "px", ani.type = "cairo")





# Load required libraries
library(ggplot2)
library(animation)

# Define the masses
masses <- data.frame(
  mass = c(10, 2, 3),
  x = c(0, -2, 4),
  y = c(0, -2, 0),
  angular_velocity = c(1, 1.5, 0.25)  # Angular velocities for each mass
)

# Create a function to rotate the masses
rotate_masses <- function(angle, angular_velocity) {
  rotation_matrix <- matrix(c(cos(angle), -sin(angle), sin(angle), cos(angle)), nrow = 2, byrow = TRUE)
  new_positions <- as.data.frame(as.matrix(masses[, c("x", "y")]) %*% rotation_matrix)
  colnames(new_positions) <- c("x", "y")
  return(cbind(masses$mass, new_positions, angular_velocity))
}

# Create initial plot
initial_plot <- ggplot() +
   geom_point(data = masses, aes(x = x, y = y, size = mass,col=as.factor(mass)))  +
  theme_void()+
  theme(legend.position = "none")+
  scale_size_continuous(range = c(3, 6)) +
  xlim(-5, 5) +
  ylim(-5, 5) +
  labs(title = "Movement of Masses")

# Create animation frames
frames <- lapply(seq(0, 4 * pi, by = pi / 36), function(angle) {
  rotated_masses <- rotate_masses(angle * masses$angular_velocity, masses$angular_velocity)
  colnames(rotated_masses) <- c("mass", "x", "y", "angular_velocity")
  frame <- initial_plot +
    geom_point(data = rotated_masses, aes(x = x, y = y, size = mass,col=as.factor(mass)))  +
    theme_void()+
    theme(legend.position = "none")
  return(frame)
})

# Save animation
ani.options(interval = 0.1)
saveGIF({
  for (i in 1:length(frames)) {
    print(frames[[i]])
  }
}, movie.name = "mass_movement.gif", ani.width = 600, ani.height = 600, ani.units = "px", ani.type = "cairo")