diff --git a/A/4/kinematics_check.py b/A/4/kinematics_check.py
new file mode 100644
index 0000000..27a03bd
--- /dev/null
+++ b/A/4/kinematics_check.py
@@ -0,0 +1,2 @@
+import loong
+loong.kPointsConsidered = 2 # Just Check the first 2 blocks to see whether it will be stuck
\ No newline at end of file
diff --git a/A/4/loong.py b/A/4/loong.py
new file mode 100644
index 0000000..fe313d8
--- /dev/null
+++ b/A/4/loong.py
@@ -0,0 +1,54 @@
+import mpmath as mp
+import numba as nb
+
+mp.dps = 25  # 设置精度为25位小数
+
+class Orbit:
+  def __init__(self):
+    self.kAlpha = mp.mpf('1.7') / (2 * mp.pi)
+  def InitIdx(self) -> mp.mpf:
+    raise NotImplementedError
+  def InitC(self) -> mp.mpf:
+    raise NotImplementedError
+  def Idx2C(self, idx) -> mp.mpf:
+    raise NotImplementedError
+  def Idx2Cartesian(self, idx) -> [mp.mpf, mp.mpf]:
+    raise NotImplementedError
+  def C2Idx(self, C:[mp.mpf, mp.mpf]) -> mp.mpf:
+    raise NotImplementedError
+  def GenerateNextPointIdx(self, cur_point_idx:mp.mpf, expected_distance:mp.mpf)->mp.mpf:
+    raise NotImplementedError
+
+class Loong:
+  def __init__(self, orbit:Orbit, total_points:int, speed:mp.mpf, delta_idx:mp.mpf):
+    self.orbit = orbit
+    self.total_points = total_points
+    self.speed = speed
+    self.delta_idx = delta_idx
+    self.kSegLength1 = mp.mpf('2.86')
+    self.kSegLength2 = mp.mpf('1.65')
+  def CalcStatusListByIdx(self, cur_idx:mp.mpf):
+    first_node_idx=cur_idx
+    first_node_C=self.orbit.Idx2C(first_node_idx)
+    first_node_dot = self.orbit.Idx2Cartesian(first_node_idx)
+    virtual_first_node_idx = first_node_idx + self.delta_idx
+    virtual_first_node_C = self.orbit.Idx2C(virtual_first_node_idx)
+    delta_T = (virtual_first_node_C - first_node_C) / self.speed
+    node_list = [{"idx": first_node_idx, "node": first_node_dot, "C": first_node_C, "v": mp.mpf('1.0')}]
+    for i in range(1, self.total_points):
+      expected_distance = self.kSegLength1 if i == 1 else self.kSegLength2
+      cur_node_idx = self.orbit.GenerateNextPointIdx(node_list[-1]["idx"], expected_distance)
+      cur_node_dot = self.orbit.Idx2Cartesian(cur_node_idx)
+      cur_node_C = self.orbit.Idx2C(cur_node_idx)
+
+      virtual_cur_node_idx = self.orbit.GenerateNextPointIdx(virtual_first_node_idx, expected_distance)
+      virtual_cur_node_C = self.orbit.Idx2C(virtual_cur_node_idx)
+      v = (virtual_cur_node_C - cur_node_C) / delta_T
+
+      node_list.append({"idx": cur_node_idx, "node": cur_node_dot, "C": cur_node_C, "v": v})
+      virtual_first_node_idx = virtual_cur_node_idx
+    return node_list
+  def CalcStatusListByTime(self, time_point:mp.mpf):
+    first_node_C = self.orbit.InitC() - time_point * self.speed
+    first_node_idx = self.orbit.C2Idx(first_node_C)
+    return self.CalcStatusListByIdx(first_node_idx)
\ No newline at end of file
diff --git a/A/4/simulator.py b/A/4/simulator.py
new file mode 100644
index 0000000..508a89d
--- /dev/null
+++ b/A/4/simulator.py
@@ -0,0 +1,40 @@
+from loong import *
+import json
+class BestOrbit(Orbit):
+  def __init__(self):
+    self.kAlpha = mp.mpf('1.7') / (2 * mp.pi)
+  def InitIdx(self):
+    return mp.mpf('0.0')
+  def InitC(self):
+    return mp.mpf('0.0')
+  def Idx2C(self, idx):
+    return idx / self.kAlpha
+  def Idx2Cartesian(self, idx):
+    return mp.matrix([mp.cos(idx), mp.sin(idx)])
+  def C2Idx(self, C):
+    return C * self.kAlpha
+  def GenerateNextPointIdx(self, cur_point_idx, expected_distance):
+    return cur_point_idx + expected_distance
+
+if __name__ == "__main__":
+  orbit=BestOrbit()
+  loong=Loong(orbit, 224, mp.mpf('2.0'), mp.mpf('1e-8'))
+  res_list=[]
+  for ti in range(-100,101):
+    print(f"calculating time_point={ti}")
+    res_list.append(loong.CalcStatusListByTime(mp.mpf(ti)))
+    # 转换成内置浮点数并保留6位
+  float_res_list = [
+    [
+      {
+        "idx": round(float(node["idx"]),6),
+        "node": [round(float(node["node"][0]),6), round(float(node["node"][1]),6)],
+        "C": round(float(node["C"]),6),
+        "v": round(float(node["v"]),6)
+      }
+      for node in res
+    ]
+    for res in res_list
+  ]
+  with open("A4_res.json", "w") as file:
+    json.dump(float_res_list, file, indent=4)
\ No newline at end of file
diff --git a/A/4/testplot.py b/A/4/testplot.py
index f595a5f..cd297d4 100644
--- a/A/4/testplot.py
+++ b/A/4/testplot.py
@@ -74,7 +74,7 @@ theta_grid = np.arctan2(Y, X)
 
 # 仅绘制半径不超过kPlotingRadius的点
 valid_points = r_grid <= kPlotingRadius
-ax.scatter(theta_grid[valid_points], r_grid[valid_points], color='red', s=10)  # 红色小点
+ax.scatter(theta_grid[valid_points], r_grid[valid_points], color='grey', s=10)  # 灰色小点
 
 plt.title("The Moving Path")