長期以來，船舶是人類主要的運輸、捕魚、和娛樂工具，所以操縱船舶是一門重要學門。但是，實船演練必須承擔昂貴的維修和油料成本，而且操作失誤也會造成人員和船體的損害。基於上述原因，船舶運動模擬器逐漸成為學習操船技術的主要輔助工具。本研究計畫將著重於發展一套物理引擎，用以開發船舶運動模擬器和電腦遊戲，增進我國的海事教育與電玩產業的發展。 在我們的研究方法中，我們將船舶視為一個系統，它內含若干參數和三個重要變數。這三個變數為船舶的重力中心、浮力中心、及定傾中心。當船舶遭受外力作用後，此三個中心的位置會變動，船舶會失去平衡，開始產生一連串運動，直到重新取得平衡為止，此種現象即為船舶運動的原理。我們歸納出船舶運動的主要外力有下列三種：波浪、船舶的承載貨物、和滲入船艙內的海水。我們在每一時間點上，估算上述外力，並減去阻尼力以求得淨力作用；然後使用牛頓運動定律，計算各種船舶運動的加速度；利用加速度，便可求得速度和位移量。最後，根據位移量，我們更新船舶的位置和姿態，並重新繪製場景，即可達到模擬船舶運動的效果。 為了方便計算外力、浮力中心、重力中心和定傾中心，我們利用三維規則網格將船體分割成許多小方塊，稱之為元素；並將船的重量、貨物和船艙的進水量分配到這些元素中。參考海水高度和波浪的起伏，我們可以算出每個元素遭受的浮力，並求得船舶的浮力中心。然後根據各元素的質量算出所有元素的質量中心，即可得船舶的重力中心。利用浮力和重力中心，可算出船舶運動的力矩，這些力矩即為外力。然後根據船體形狀，我們算出阻尼力與淨作用力，進而推算出各種運動的加速度、速度和位移量。 When a ship floats on the sea surface, its stability is mainly influenced by the sea waves, the cargo-loads, and the flooding water inside its body. Any variations in these factors will cause the ship to heave, roll, and pitch. These motions produce significant visual effects through which we comprehend the hydrodynamic behaviors of the ship. In this proposal, we propose a research project on the real time simulation of ship motions under the influences of sea waves, cargo-loads, and flooding water. The governing equations of ship motions are very complicated, it is impossible to compute ship motions in real time. Therefore, alternative approaches have to be utilized for ship motion calculation. In this research, we model a ship as a system. This system contains three major variables, which include the meta-center, gravity center, and buoyancy center of the ship. This system is influenced by external and internal forces. The internal forces are produced by the ship's propellers and rudders. These internal forces drive the ship forward and change the course direction of the ship. The external forces are created by the sea waves surrounding the ship, and the cargos and flooding water inside the ship. These external forces change the gravity center, buoyancy center, and meta-center. Thus the ship loses its stability and starts to heave, roll, and pitch. In one of our previous research, we had successfully designed physical models for ship motions. However, these models cannot be used to simulate the stability variation of ship. Therefore, we formulate this research project to design numerical procedures to simulate ship motions. In the proposed method, the ship body is split into cells by using a regular grid at first. The ship mass, the cargoes, and the flooding are distributed to these cells. Then the ship body is split into slices in the x, y, and z directions. The gravity center, buoyancy center, and meta-center of the ship are computed on the fly by using basic physical laws. Based on the positions of these three centers, the external forces for ship motions are measured. By using the second Newton's Law, the accelerations and velocities of ship motions are calculated. In turn, the motion magnitudes are obtained by multiplying the velocities with the time step size. Finally, the orientation and position of the ship are updated, and the scene is rendered again. Our ship motion models can be used to build a physics engine for ship handling simulation system and computer games. Therefore, this research will produce significant contribution in education and entertainment.