A hybrid system including: an internal combustion engine of a vehicle; and a stirling engine (400, 10) mountable on the vehicle for use with an exhaust system of the internal combustion engine as a heat source, said stirling engine (400, 10) comprising: a heater (405, 47) arranged to draw heat from the exhaust system of the internal combustion engine, a cylinder (401, 22), wherein a working fluid heated by the heater (405, 47) flows into a space above the cylinder (401, 22), a piston (402, 21) reciprocating inside the cylinder (401, 22) while keeping an air-tight condition between the piston (402, 21) and the cylinder (401, 22) by means of a gas bearing (412, 48) which supports the piston (402, 21) inside the cylinder (401, 22) with no piston ring, using the pressure of distributed gas generated at a minute clearance formed between the piston (402, 21) and the cylinder (401, 22), a crankshaft rotating around a driving shaft, an extension extending downward from the piston, a connecting rod coupling the extension and the crankshaft, and a linear approximation mechanism (310, 50) coupled directly or indirectly to the piston (402, 21) to make an approximately linear motion when the piston (402, 21) reciprocates inside the cylinder (401, 22), wherein the linear approximation mechanism is coupled to a coupling element between the extension and the connecting rod to control movement of the coupling element so that the coupling element makes an approximately linear motion along an axial centerline of the cylinder. an internal combustion engine of a vehicle; and a stirling engine (400, 10) mountable on the vehicle for use with an exhaust system of the internal combustion engine as a heat source, said stirling engine (400, 10) comprising: a heater (405, 47) arranged to draw heat from the exhaust system of the internal combustion engine, a cylinder (401, 22), wherein a working fluid heated by the heater (405, 47) flows into a space above the cylinder (401, 22), a piston (402, 21) reciprocating inside the cylinder (401, 22) while keeping an air-tight condition between the piston (402, 21) and the cylinder (401, 22) by means of a gas bearing (412, 48) which supports the piston (402, 21) inside the cylinder (401, 22) with no piston ring, using the pressure of distributed gas generated at a minute clearance formed between the piston (402, 21) and the cylinder (401, 22), a crankshaft rotating around a driving shaft, an extension extending downward from the piston, a connecting rod coupling the extension and the crankshaft, and a linear approximation mechanism (310, 50) coupled directly or indirectly to the piston (402, 21) to make an approximately linear motion when the piston (402, 21) reciprocates inside the cylinder (401, 22), a heater (405, 47) arranged to draw heat from the exhaust system of the internal combustion engine, a cylinder (401, 22), wherein a working fluid heated by the heater (405, 47) flows into a space above the cylinder (401, 22), a piston (402, 21) reciprocating inside the cylinder (401, 22) while keeping an air-tight condition between the piston (402, 21) and the cylinder (401, 22) by means of a gas bearing (412, 48) which supports the piston (402, 21) inside the cylinder (401, 22) with no piston ring, using the pressure of distributed gas generated at a minute clearance formed between the piston (402, 21) and the cylinder (401, 22), a crankshaft rotating around a driving shaft, an extension extending downward from the piston, a connecting rod coupling the extension and the crankshaft, and a linear approximation mechanism (310, 50) coupled directly or indirectly to the piston (402, 21) to make an approximately linear motion when the piston (402, 21) reciprocates inside the cylinder (401, 22), wherein the linear approximation mechanism is coupled to a coupling element between the extension and the connecting rod to control movement of the coupling element so that the coupling element makes an approximately linear motion along an axial centerline of the cylinder.