Problem: C++ Vehicle Dynamics Coriolis and Lateral Force Calculation

The problem aims to develop C++ template functions for vehicle dynamics force calculations, covering simplified Coriolis plus centripetal force and comprehensive lateral resultant force involving Earth rotation related terms. The functions support both single and batch vehicle parameter input, return structured function pointers for practical vehicle dynamics analysis applications.


Input/Output: The problem receives two categories of input: first, a user-defined C++ struct type VehicleParams as the template parameter for the required template functions, which contains four double-type fields: latitude (in degrees), vehicle mass, driving velocity, and turning radius; second, predefined global fixed constants including PI = 3.14159265358979323846, OMEGA = 7.292e-5 rad/s, R_EARTH = 6.371e6 m for force calculation.
For subproblem 7.1, the problem outputs a struct holding a function pointer that takes a single VehicleParams instance as input and returns the sum of simplified Coriolis force and centripetal force as a double value. For subproblem 7.2, the problem outputs a struct holding two function pointers: one processes a single VehicleParams input to calculate lateral resultant force covering Coriolis, centrifugal, and Earth rotation related terms, the other processes batch input of std::vector<VehicleParams> and returns a std::vector<double> of corresponding calculation results. The template functions are instantiated with the input VehicleParams type to generate callable function pointers for specified force computing tasks.

Required dependencies:

Sub-steps:
step_number: 1
step_description_prompt: Please use C++ to generate the template function subproblem_7_1_functions with VehicleParams as its template parameter. It implements simplified Coriolis force plus centripetal force calculation for vehicle dynamics, takes vehicle parameters including latitude, mass, velocity, turning radius as input, uses constants PI and OMEGA=7.292e-5, returns a struct holding the corresponding calculation function pointer.
function_header: auto subproblem_7_1_functions() {
    struct Result
test_cases: int main() {
    struct VehicleParams {
        double latitude;
        double velocity;
        double mass;
        double turning_radius;
    };
    
    unsigned int seed = 12345;
    srand(seed);
    
    std::cout << "Problem 7.1\n";
    
    auto funcs = subproblem_7_1_functions<VehicleParams>();
    auto sw_f = funcs.sw_f;
    
    bool test1_passed = false, test2_passed = false, test3_passed = false;
    
    // Test 1: Vehicle at equator, low speed, large turning radius
    {
        VehicleParams params;
        params.latitude = 0.0;
        params.velocity = 20.0;
        params.mass = 1500.0;
        params.turning_radius = 100.0;
        
        double result = sw_f(params);
        double expected = 6000.0;
        double tolerance = 0.1;
        if (std::abs(result - expected) < tolerance) {
            test1_passed = true;
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    // Test 2: Vehicle at mid-latitude, highway speed, moderate turning radius
    {
        VehicleParams params;
        params.latitude = 30.0;
        params.velocity = 25.0;
        params.mass = 2000.0;
        params.turning_radius = 150.0;
        
        double result = sw_f(params);
        double expected = 8336.979;
        double tolerance = 1.0;
        if (std::abs(result - expected) < tolerance) {
            test2_passed = true;
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    // Test 3: Vehicle at high latitude, high speed, small turning radius
    {
        VehicleParams params;
        params.latitude = 60.0;
        params.velocity = 40.0;
        params.mass = 1800.0;
        params.turning_radius = 80.0;
        
        double result = sw_f(params);
        double expected = 36009.094;
        double tolerance = 1.0;
        if (std::abs(result - expected) < tolerance) {
            test3_passed = true;
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    if (test1_passed && test2_passed && test3_passed) {
        std::cout << "Completely Correct！\n";
    }
    
    return 0;
}

step_number: 2
step_description_prompt: Please use C++ to generate a template function named subproblem_7_2_functions with typename VehicleParams as the template parameter. This function computes vehicle lateral resultant force involving Coriolis, centrifugal and Earth rotation related terms, and returns a struct holding two function pointers for single input and batch input processing respectively.
function_header: auto subproblem_7_2_functions() {
    struct Result
test_cases: int main() {
    struct VehicleParams {
        double latitude;      
        double velocity;      
        double mass;          
        double turning_radius;
    };
    
    unsigned int seed = 12345;
    srand(seed);
    
    std::cout << "Problem 7.2\n";
    
    auto funcs = subproblem_7_2_functions<VehicleParams>();
    auto sw_f = funcs.sw_f;
    auto sw_f_batch = funcs.sw_f_batch;
    
    bool test1_passed = false, test2_passed = false, test3_passed = false;
    
    // Test 1: Batch calculation for vehicles at different latitudes with same speed and mass
    {
        std::vector<VehicleParams> vehicles = {
            {0.0, 25.0, 1500.0, 80.0},    
            {30.0, 25.0, 1500.0, 80.0},   
            {60.0, 25.0, 1500.0, 80.0}    
        };
        
        std::vector<double> results = sw_f_batch(vehicles);
        
        const double DEG2RAD = PI / 180.0;
        
        std::vector<double> expected;
        for (const auto& v : vehicles) {
            double phi_rad = v.latitude * DEG2RAD;
            double term1 = 2.0 * v.mass * v.velocity * OMEGA * sin(phi_rad);
            double term2 = v.mass * v.velocity * v.velocity / v.turning_radius * cos(phi_rad);
            double term3 = v.mass * OMEGA * OMEGA * R_EARTH * cos(phi_rad) * cos(phi_rad);
            expected.push_back(term1 + term2 + term3);
        }
        
        double tolerance = 10.0;
        test1_passed = (results.size() == expected.size());
        for (size_t i = 0; i < results.size() && test1_passed; ++i) {
            test1_passed = test1_passed && (std::abs(results[i] - expected[i]) < tolerance);
        }
        if (test1_passed) {
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    // Test 2: Batch calculation for mixed vehicle fleet with varying parameters
    {
        std::vector<VehicleParams> vehicles = {
            {-45.0, 15.0, 1200.0, 150.0},  
            {0.0, 30.0, 1800.0, 100.0},    
            {45.0, 40.0, 2200.0, 60.0}    
        };
        
        std::vector<double> results = sw_f_batch(vehicles);
        
        test2_passed = (results.size() == vehicles.size());
        for (size_t i = 0; i < vehicles.size() && test2_passed; ++i) {
            double expected = sw_f(vehicles[i]);
            double tolerance = 1.0;
            test2_passed = test2_passed && (std::abs(results[i] - expected) < tolerance);
        }
        
        for (size_t i = 0; i < results.size() && test2_passed; ++i) {
            test2_passed = test2_passed && (results[i] > 0);
        }
        
        if (test2_passed) {
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    // Test 3: Batch calculation for high-speed vehicles at extreme latitudes
    {
        std::vector<VehicleParams> vehicles = {
            {80.0, 55.0, 2000.0, 40.0},   
            {-80.0, 55.0, 2000.0, 40.0},  
            {0.0, 55.0, 2000.0, 40.0}    
        };
        
        std::vector<double> results = sw_f_batch(vehicles);
        
        const double DEG2RAD = PI / 180.0;
        
        std::vector<double> expected;
        for (const auto& v : vehicles) {
            double phi_rad = v.latitude * DEG2RAD;
            double term1 = 2.0 * v.mass * v.velocity * OMEGA * sin(phi_rad);
            double term2 = v.mass * v.velocity * v.velocity / v.turning_radius * cos(phi_rad);
            double term3 = v.mass * OMEGA * OMEGA * R_EARTH * cos(phi_rad) * cos(phi_rad);
            expected.push_back(term1 + term2 + term3);
        }
        
        double tolerance = 50.0;
        test3_passed = (results.size() == expected.size());
        for (size_t i = 0; i < results.size() && test3_passed; ++i) {
            test3_passed = test3_passed && (std::abs(results[i] - expected[i]) < tolerance);
        }
        
        if (test3_passed) {
            double diff = std::abs(results[0] - results[1]);
            test3_passed = test3_passed && (diff < 200.0); 
        }
        
        if (test3_passed) {
            std::cout << "correct\n";
        } else {
            std::cout << "wrong\n";
        }
    }
    
    if (test1_passed && test2_passed && test3_passed) {
        std::cout << "Completely Correct！\n";
    }
    
    return 0;
}

General solution:

General tests: