International Science Community Association Research Journal of Mathematical and Statestical Sciences 14 3 2026 09 12 Phase Plane Stability of Damping Regimes in a Vehicle Suspension System 10 13 EN Pankratov E.L. 1 Nizhny Novgorod State Agrotechnical University, 97 Gagarin Avenue, Nizhny Novgorod, 603950, Russia Rawan Sunil 1 Department of Mathematics, Balganga Degree College, Sendul, Kemar, Sri Dev Suman Uttarakhand University, Tehri Garhwal, Uttarakhand, India, 249155 A. Devika 1 Department of Mathematics, Nrupathunga University, Bengaluru, India S.B. Sowmya 2 Department of Mathematics, Nrupathunga University, Bengaluru, India > Research Paper 2026 4 10 2026 09 12 This study looks at phase plane portraits of vehicle suspension dynamics. It creates three distinct trajectory patterns: spiral, straight radial, and curved. These patterns reflect important suspension behaviors in different types of vehicles. These mathematical patterns directly inform real driving experiences. Spiral trajectories, common in sports cars, provide quick handling for fast turns and better road feel. Straight radial trajectories, typical of family sedans, provide balanced performance and quick stabilization after road disturbances, making them perfect for daily driving. Curved trajectories in trucks and luxury vehicles help them respond smoothly to uneven surfaces. This design ensures comfort and stability, especially during long drives or when carrying heavy loads. The research gives engineers, mechanics, and manufacturers visual tools. They can use these tools to check suspension features and pick the right shock absorber setups. Linking trajectory shapes to vehicle performance needs to optimize tuning, boosts safety, and cut down component wear. Engineers like math validation. Mechanics benefit from intuitive diagnostic guides. Manufacturers gain better design efficiency. This work combines theory with real-world car applications. It helps design better suspension systems for specific vehicle functions and driving conditions. Copyright@ International Science Community Association